WASHINGTON — One of the biggest challenges to ending the foreclosure crisis is this: A surprising number of homeowners who get their monthly payments reduced fall behind again within a year.

When borrowers get into financial trouble, lenders have several ways to help. They can offer grace periods, longer repayment schedules, lower interest rates or reduced balances.

But nearly 40 percent of homeowners who had their monthly payments cut by 20 percent or more last year were delinquent again within a year, according to a report Monday from the Office of the Comptroller of the Currency and the Office of Thrift Supervision.

With the economy still weak and employers continuing to cut jobs, “Even if you’ve gone through a modification, your situation may deteriorate,” said Fred Phillips-Patrick, director for credit policy at the thrift office.

That’s an ominous sign for the Obama administration’s plan to stem the foreclosure crisis. Lenders participating in the program have offered trial loan modifications to 760,000 eligible borrowers since it was launched in March. As of last month, just 31,000 of them had been made permanent, which requires at least three on-time payments and proof of income. Nearly the same number had dropped out of the program or were found to be ineligible.

The meager success rate means the $75 billion program may bring little relief to struggling homeowners. A record 14 percent of homeowners with a mortgage are either behind on their payments or in foreclosure. And that affects many more homeowners because deeply discounted foreclosures are hurting property values in many parts of the country, especially Arizona, California, Florida and Nevada.

But regulators Monday pointed to some encouraging signs among loans modified from April through June of this year.

About 20 percent of those borrowers had missed at least two out of three payments. That’s far better than the track record of loans modified during the same three months a year earlier. About 35 percent of those borrowers were delinquent within three months.

The report also found that lenders completed about 31,000 short sales—ones in which the sales price is lower than the mortgage balance—in the July- September quarter. While that’s up 22 percent from the prior quarter, lenders foreclosed on nearly four times as many homes.