More than a third of the 1.24 million borrowers who have enrolled in the $75 billion mortgage modification program have dropped out. That exceeds the number of people who have managed to have their loan payments reduced to help them keep their homes.

Last month alone,155,000 borrowers left the program — bringing the total to 436,000 who have dropped out since it began in March 2009.

About 340,000 homeowners have received permanent loan modifications and are making payments on time.

Administration officials say the housing market is significantly better than when President Barack Obama entered office. They say those who were rejected from the program will get help in other ways.

But analysts expect the majority will still wind up in foreclosure and that could slow the broader economic recovery.

A major reason so many have fallen out of the program is the Obama administration initially pressured banks to sign up borrowers without insisting first on proof of their income. When banks later moved to collect the information, many troubled homeowners were disqualified or dropped out.

Many borrowers complained that the banks lost their documents. The industry said borrowers weren’t sending back the necessary paperwork.

Carlos Woods, a 48-year-old power plant worker in Queens, N.Y., made nine payments during a trial phase but was kicked out of the program after Bank of America said he missed a $1,600 payment afterward. His lawyer said they can prove he made the payment.

Such mistakes happen “more frequently than not, unfortunately,” said his lawyer, Sumani Lanka. “I think a lot of it is incompetence.”

A spokesman for Bank of America declined to comment on Woods’s case.

Treasury officials now require banks to collect two recent pay stubs at the start of the process. Borrowers have to give the Internal Revenue Service permission to provide their most recent tax returns to lenders.

Requiring homeowners to provide documentation of income has turned people away from enrolling in the program. Around 30,000 homeowners started the program in May. That’s a sharp turnaround from last summer when more than 100,000 borrowers signed up each month.

As more people leave the program, a new wave of foreclosures could occur. If that happens, it could weaken the housing market and hold back the broader economic recovery.

Even after their loans are modified, many borrowers are simply stuck with too much debt — from car loans to home equity loans to credit cards.

“The majority of these modifications aren’t going to be successful,” said Wayne Yamano, vice president of John Burns Real Estate Consulting, a research firm in Irvine, Calif. “Even after the permanent modification, you’re still looking at a very high debt burden.”