As the final days of 2012 slipped away, Lisa Price made her client an offer she thought he couldn’t refuse. Her client — we’ll call him John Doe — was paying a rate of 6.616% on his $435,000 mortgage, with 25 years left to go. Price, a mortgage banker for Quicken Loans, offered to refinance his loan at 4.125%, keeping the 25-year payout time. The deal would have knocked his monthly payments down to $3,383, a savings of $630 a month. Closing costs were minimal and would have been recouped through the savings within four months of signing. And with the streamlined process she proposed, it would have required very little paperwork and wasn’t contingent on any appraisal valuation. It seemed like a no-brainer. But John Doe said no thanks.

“It didn’t make any sense,” says a stunned Price, reflecting on the rejection. “Usually when I call someone with a deal like that they’re really excited.”

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It’s typically pretty easy for mortgage brokers to give away money, and indeed, refinancing activity has skyrocketed as interest rates plummeted in recent years. The one group of homeowners who didn’t participate in the refi boom — those whose home prices tanked, leaving them without enough equity in their home to qualify for refinancing — are now eligible to restructure their loans thanks to a new government program. But as Quicken Loans and other mortgage originators have learned, it can be surprisingly difficult to persuade some of these people to take sweet deals like the one above, even when the government is greasing the skids.

The first government assistance programs after the housing bubble burst offered to help homeowners only after they stopped paying their mortgages. But a later program — the Home Affordable Refinance Program (HARP) — was designed specifically to help out those underwater homeowners still paying their mortgages on time by giving them access to the low rates so many others are enjoying. HARP has been refined several times since its inception in 2010, and every version of the plan has made it easier for homeowners to qualify. But getting the word out hasn’t been easy.

Quicken and other mortgage originators have aggressively tried to let homeowners who qualify know about the program. “We get their home number, the business number, their e-mail, we express-mail packages to their house so it looks serious,” says Dan Gilbert, founder and chairman of Quicken. “We leave messages; we tell them, ‘Go look up HARP on Google and you’ll see it’s real.’ We don’t quit.” And yet almost half of these homeowners don’t respond. “If you would have told me all the facts about how this works before, I would have predicted we’d get 80% to 85%,” Gilbert marvels.

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Ultimately, Quicken says, only about 25% of the homeowners who qualify for HARP actually end up refinancing. And that’s the shame of it all. HARP is a smart program. It rewards good behavior — those who have continued to pay their mortgages — while lending a helping hand to those who could really use it. And it attempts to even the playing field by giving more Americans fair access to the low interest rates enjoyed by big businesses and the wealthy. This program is also good for the economy, as consumers spend much of the money they save on their mortgage payments.

So how do the government and mortgage originators convince the public to take advantage of a program that can truly help many who need it? It’s the classic lesson of once bitten, twice shy. Wounds from all those no-money-down loans and balloon payments have yet to heal for the homeowners bitten when the housing bubble burst. Others still feel the sting of paying hundreds for appraisals in an attempt to refinance, only to be spurned when their homes were valued at less than they owed on the mortgage. It may be hard for those consumers to trust again anytime soon. But for those with the courage to give it another go, love might actually be better the second time around.

This story is from the February 25, 2013 issue of Fortune.