Consider the Winnebago. Just five years ago, the brontosaurus of consumer vehicles looked as if it might be on the point of extinction. Sales had been sliding for several years before plunging off a precipice as the financial crisis deepened into a global recession in 2009. That year Winnebago Industries tallied $211 million in sales, less than a fifth of the 2004 figure. The whole recreational vehicle (RV) industry appeared to be wheezing toward its demise. In what seemed like seconds, 20 players closed or were acquired. That’s why it’s so surprising to see Winnebago on Fortune’s list of Fastest-Growing Companies—it’s No. 56 in 2014—for the second year in a row. (Or perhaps not so surprising, as we’ll see.) Sales have come roaring back with the recovery—to $803 million last year, and $884 million in the most recent four quarters—though not yet to their peak a decade ago. The company’s market share has surged from 17.2% to 20.3% in the 12 months that ended in May, according to data provider Statistical Surveys. (Thor Industries is No. 1 with 24.6%.)

It would be easy to dismiss this as the latest boomlet in an industry famous for its cycles, were it not for a demographic tidal wave—the so-called silver tsunami—that has already begun: The retirement of America’s 76 million baby boomers. The largest group of U.S. retirees in history has entered its prime RV-buying years, and Winnebago thinks it has precisely the right mix of nostalgia, adventure, and cushy comfort they’re yearning for.

ALSO SEE: Winnebago Industries through the ages

That thinking was visible in April at Winnebago’s annual Dealer Days, at which the company rolls out its newest motor homes. The convention’s most anticipated event brought hundreds of RV dealers and a handful of financial analysts to a darkened hall in Las Vegas’s Mirage Hotel. By its reserved standards—Winnebago is self-effacing in just the way you might expect a small-town Iowa company to be (and I say that as a native of Cedar Rapids)—the company lit up the joint. There were flashing lights, and “The Age of Aquarius,” the Fifth Dimension’s hit song from the musical Hair, exploded just as the drapes fell to reveal a pair of boxy, upright RVs. To the untrained eye, they could have passed for shiny bread trucks. But this was a knowledgeable audience: There were gasps, a few whistles, and the roar of applause.

The crowd-pleasing vehicle was the 2015 Brave, a model that harks back, in name and aesthetics, to the iconic motor home of the company’s heyday. Introduced in 1970, the original Brave became the company’s first sensation, easily recognized by its “flying W” logo and its bunk-over-the-cabin “eyebrow.” (Until 1966, the company made only trailers.)

The modern Brave has all those retro trappings and then some: It comes in three color schemes (Mello Yellow, Crimson ’n Clover, and Woodstock), with a choice of Cherry Cola or Cream Soda cabinetry. If those aren’t enough historical allusions for you, there are also psychedelic, Peter Max–lite graphics on the website promoting the $95,000 vehicle.

WIN01_2 Ryan Donnell

Of course, the retro elements are limited to matters of style. The Brave’s toys and accoutrements are very much of the moment: a flat-screen TV, a bunk with power lift, and a Murphy-style sofa bed that can even convert to a dining table.

“Do you like it? Did it make you smile?” Winnebago CEO Randy Potts asked me eagerly when I mentioned the Brave on a recent visit to the company’s headquarters in Forest City, in the heart of north Iowa farmland. The vehicle is something of a labor of love for the company, subject of a two-year creative process in which plans were scrapped more than once and its rollout delayed. Orders have poured in for the Brave, and Potts talks about it like a pleased, if still affirmation-seeking, parent. He says he told his team, “We only have one chance with this. This has to be something that makes people happy because of the memories.”

People with lots of memories (a.k.a. retirees) are the company’s sweet spot, and they make for a loyal and engaged customer base. Witness the 11,500-strong members of the company’s Winnebago-Itasca Travelers Club, who socialize at spirited rallies across the country. According to the club web page, optional activities include “cow-chip tossing,” a pastime that apparently predates even the Age of Aquarius. The company says it is also encouraging bicycling events and other more contemporary pursuits.

Company executives aren’t about to ballyhoo the kinds of sales they think the Brave could deliver. They’re too diffident for that sort of boasting. About as much as they’re willing to allow is that the company could benefit from a “favorable demographic trend.” But Winnebago thinks it could be a hit. If so, the company just might be able to break out of the boom-and-bust cycles that have trapped it for decades.

The ERA of the original Brave was a heady one for Winnebago. In 1971, its first full year as a public company, its stock rose more than any other, by 470%, according to the company’s museum. For a time Forest City, whose population hovers near 4,000, claimed more millionaires per capita than any other place in the U.S.

Winnebago owes its existence to John Hanson, a Forest City mortician and camping enthusiast. Hanson was a civic-minded fellow, and back in the 1950s he worried that his hometown lacked industry and was losing young people who no longer wanted to work on farms. Looking to breathe life into the local economy, Hanson and others coaxed a California travel-trailer company to set up a factory in Forest City. It folded within a year, and in 1958, Hanson took over. He named the company Winnebago for Forest City’s river, which itself was named for the Native Americans who originally inhabited the area.

Hanson also ran his family’s furniture business, and he saw synergies with Winnebago. He outfitted the trailers with finer furnishings and sturdier walls, building the reputation for quality products that the company still carries today. (Hanson died in 1996, after retiring and retaking the reins several times.)

With the Brave, Winnebago took off, and motor homes quickly became the company’s mainstay. The industry peaked in 1977, when U.S. shipments reached 160,200. During that period, Winnebago introduced a nearly identical second brand, Itasca, to maximize the company’s showroom space in independent dealerships.

Things have never again been so sweet. The energy crisis gave way to an endless cycle of ups and downs, with sales bottoming out anytime fuel prices soared or the economy tanked. (So reliable is the pattern that RV sales are considered a leading economic indicator.) Winnebago learned to adapt: To protect its low-volume business in lean times, the company stopped carrying inventory and debt, the latter of which sometimes irritated investors.

Then came 2009. Just 13,000 motor homes shipped industrywide, less than a quarter of the 55,000 in 2007. Winnebago was pounded. The company shuttered facilities and laid off more than half its 4,000-plus workforce.

Potts, 55, an unassuming Iowa native and engineer, became CEO in 2011, 28 years after he started as a temporary tool designer at Winnebago. He saw in those dark days a rare and valuable opportunity to reshape the company. “I would get on my soapbox,” he says, “and preach to my top management group, ‘This is probably one chance you’ll have in your life to regrow a business in your vision.’”

To visit Winnebago Industries is in some ways to enter a time warp. Let’s start in Forest City, where Winnebago’s sizable campus makes up the southern part of town. Near one of the factory gates is the intersection of Winnebago Way and John K. Hanson Drive. Across the street is the Winnebago Industries’ Visitors Center; nearby is Winnebago’s Activity Complex. It’s not much of a stretch to say Winnebago is Forest City: In town you’ll find tiny Waldorf College and a business district that has thinned down to a quilt store, gas stations, a Dollar General, a Subway outlet, and not much more.

Winnebago’s modest, low-slung headquarters—Potts occupies a windowless corner office on the second floor—sits at the center of campus, largely obscured by warehouses and rows of motor homes in various stages of production. Big Bertha, the largest production facility, where most of Winnebago’s 2,500 Forest City employees (average tenure: 12 years overall, 17 years for management) work, looms especially large.

Many RV manufacturers assemble vehicles from parts made by other companies. By contrast, Winnebago manufactures almost everything itself—from the aluminum extrusions and plastic moldings used for parts to cabinetry and countertops to the bedspreads and other soft goods that come out of the stitch-craft factory. (The company doesn’t make the chassis.)

Winnebago’s facilities have a whimsical, Willy Wonka quality to them; metal parts loop around one factory on an elevated conveyor belt from which they are dunked in paint, dried in an oven, then hand-delivered to their eventual workstation. Meanwhile people, not machines, prepare 100-pound looms of wire, shave down RV doors, affix Winnebago decals, and put furnishings in place. Every motor home is made to order. (The company, which produces anywhere from 12 to 50 per day, offers 28 models and 88 floor plans.)

WIN01_3 Ryan Donnell

Part of Potts’s role seems to be to apply some basic management initiatives to this (appealingly) anachronistic operation. As Winnebago began to recover and ramp up after 2009, he refrained from investing in new plants, even as the company began to run out of room in Forest City. Instead, he struck a deal with officials of Lake Mills, a neighboring town, to make use of an abandoned city-owned building. Pledging to bring 50 jobs, Winnebago negotiated a five-year lease for $1 a year.

Potts has begun considering more exceptions to Winnebago’s long tradition of vertical integration. The company now carefully analyzes whether it makes sense to make each part itself. Winnebago has begun outsourcing smaller fiberglass components, for example, to save money.

In other ways, Potts’s post-recession leadership has been focused on shaking things up. He rejiggered the company’s structure. Product managers rather than engineers now call the shots on new vehicles, a move that Potts made to increase responsiveness to consumers and to cut the blame game that ensued when vehicles didn’t sell. (Engineers would point to bad sales tactics; salespeople would point to design flaws.) Winnebago is also moving away from the traditional concept of model years—if consumers have complaints or find ways to improve their vehicles, the company won’t wait until the next model comes out to fix them.

Potts also hired outsiders, notably Scott Degnan, a veteran of California RV manufacturer Fleetwood, who became the company’s VP of sales and product management in 2012. Degnan says he arrived unafraid of “ruffling feathers.”

HOW FAR TO THE PEAK? Winnebago's annual revenues HOW FAR TO THE PEAK? Winnebago’s annual revenues

Feathers, it appears, are easily ruffled at Winnebago. The new regime raised the hackles of some company veterans and dealers by putting Winnebago branding on its Itasca models. As Degnan puts it, that “has pushed some people into a very uncomfortable place.” The day I visited, Degnan noted that something as seemingly minor as the location of a temporary sticker on the corner of the Brave’s windshield—the wiper, when in use, touches its edge—struck some longtime employees as a violation of a policy on preserving an unimpeded view. It ain’t easy being an icon.

Winnebago, known for its premium, big-ticket motor homes (selling for well over $100,000), has been introducing new products at lower price points, better suited to the post-recession marketplace. It branched into Class B motor homes (also known as “camper” or “conversion” vans) in 2008 and added smaller Class C models that go for as little as $60,000 each. The company also added a number of floor plans and emphasized features, such as slide-out rooms and fold-up beds, that appeal to the modern, more active RV-er.

Degnan says the goal is to rise above the “sea of sameness” among RVs with innovative, fuel-efficient chassis and striking design. The Brave may not seem particularly bold to the uninitiated. Yet it stands out in an industry where every motor home looks as though it’s dressed for duck hunting: a muted, earth-tone box with similar swirling motifs. By those standards the goofy and colorful Brave has real personality. Its interiors challenge the drab RV color palettes with bright accents, and the use of booth seating confers hints of a diner’s atmosphere.

Winnebago already has one new-generation hit: the Travato, a camper van that comes in a sporty red or silver with bike and kayak racks. It has become a top seller for the company, and management hopes the Travato might lure some younger customers. With that in mind, Winnebago has also gotten back into trailers—they start at $15,000 and are both a larger market and a gateway product—by acquiring SunnyBrook in 2010. Potts doesn’t have big ambitions for that competitive market, and the business is only just beginning to pick up, but he wants the brand to be there for the exposure.

Getting more mileage out of the company’s iconic brand is part of Potts’s growth plan. The company is working on licensing deals that will soon result in Winnebago-brand camping and tailgating gear.

All of this gives classic old Winnebago a fresh (or in the case of the Brave, retro) look, but the company is hardly giving up its old tricks. The economy is looking sturdier, and those favorable demographic tailwinds are picking up. That same April at Dealer Days, Winnebago unveiled the 42-foot long, $420,000 Grand Tour. With an electric fireplace, a ceiling fan, and a bed festooned with a half-dozen throw pillows, it’s Winnebago’s most luxuriously outfitted motor home yet. Potts certainly wants to avoid (or at least soften) the next bust. But there’s no reason not to enjoy the current boom as much as he can.

This story is from the September 1, 2014 issue of Fortune.