Google’s stock is on its steepest decline ever, a sign that investors who once believed in the search giant’s story of perpetual growth have started to lose faith.

There’s certainly some immediate cause for concern. Google’s revenue growth is rapidly decelerating — more rapidly than would be accounted for by its sheer size. Last year’s annual growth rate of 56.5% has now dropped to 28.27%, according to Thomson Financial. And its stock price, the best measure of investors’ perception of future growth, is taking a beating of historic proportions. Google’s shares slid from a 52-week high of $747 last November to $475 on Thursday’s close, lopping more than $85 billion off its market cap in the space of three months.

Analysts say it’s not yet time to freak out. Betting against Google, they say, is a bit like betting against Tiger Woods.

“Google is not falling off a cliff,” said Lehman Bros.’ Doug Anmuth. “For the past six months or so, the broad consensus is that Google would be somewhat impacted by a recession. It’s not immune, but Google would certainly hold up a lot better than most.”

To be sure, an economic slowdown — and a fall-off in advertising dollars — probably wouldn’t hurt Google (GOOG) as much as, say, newspapers and glossy magazines. But some are asking a more fundamental question. They want to know whether Google’s growth engine is running out of gas.

“Google hit the bull eye’s with search,” said Iggy Fanlo, CEO of AdBrite, referring to the business of selling ads for Hertz based on the auction of key search terms, such as “rental car.” “Google has this square peg that they’ve been fitting into this square hole.”

But there are signs that the market for search ads may be approaching saturation. Much of this week’s losses can be traced to a comScore report that found that clicks on Google’s ads in January were flat. Google had warned that it has been rooting out fraudulent and accidental clicks, which probably accounts for some of that weakness. But it may not account for all of it.

The deeper problem for Google is that many investors perceive it as a one-trick pony. Most of Google’s ancillary ventures — Google maps and docs and the like — are loss leaders. For real revenue growth, Google has been trying to build a business in display advertising — like the banner ads that appear in social networks and other venues. But they’re finding that it’s not as easy as it looks. “Some of the monetization work we were doing [on MySpace] didn’t pan out as well as we had hoped,” admitted Sergey Brin, Google’s cofounder, during the company’s fourth quarter earnings call.

The trick, experts say, is to put ads on the screen that reflect customers’ interests, something that goes beyond simply knowing what context they’re being viewed in.

“Contextual advertising isn’t the right thing for most of the Internet,” says AdBrite’s Fanlo. “It’s like selling Superbowl ads. They don’t sell me cleats, jerseys or helmets. They sell me cars, beer, and erectile dysfunction medication because they know I’m an old, fat guy.”

Fanlo says most advertisers are better off targeting customers based on where they live, who they are, and how they surf the web.

Another problem for Google is that although tech-savvy advertisers are eager to expand their marketing dollars beyond paid search, they’re not willing to spend those dollars blindly. They want tools and reporting systems that help them target display ads and accurately track their effectiveness.

In other words, advertisers now want the business of buying display ads to be as transparent as Google’s paid click system.

“Google is the leader of accountability. Consumers type in keywords into the search box. They click on ads, and clients are happy. But more and more, we’re seeing clients who want to know the relationship between advertising on Google and the brand messaging,” said Rob Norman, CEO of GroupM Interactive, a holding company of WPP. “There’s a perceived value and an actual value of online advertising, and our job is to help clients navigate that.”

It was to provide such tools that Google made its $3.1 billion bid for ad-service leader DoubleClick, a deal that has been approved but not yet consummated.

Meanwhile, Google’s search ad business, while not growing as fast as it was, continues to make money.

“A 4% drop in the stock based on the day’s news doesn’t show any fundamental problems in the ad model,” says Michael Ostrovsky, assistant professor of economics at Stanford. “This is a very sound model. Maybe some of the rules of how keywords are being auctioned will change, but the fundamental ideals of how Google sells ads is going to stay for a long time.”