WASHINGTON – The Obama administration’s flagship mortgage-relief effort is failing to ease the foreclosure crisis as more than half of those who have enrolled have fallen out of the program.

As of August, approximately 680,000 homeowners who applied to get their mortgage payments lowered, or about 51 percent, have been disqualified, the Treasury Department said Wednesday. That’s up from about 48 percent in July.

The report gives ammunition to critics who say the program has failed to slow the tide of foreclosures. They say it’s better to let troubled homeowners lose their homes and home prices fall.

“The problem is just so huge in magnitude that there’s no viable solution that can come out of the government to solve it,” said Anthony Sanders, a finance professor at George Mason University.

About 2.5 million homes have been lost to foreclosure since the recession started in December 2007, according to RealtyTrac Inc.

Foreclosures and distressed sales are a major reason the economy has struggled to regain its footing after the recession ended in June 2009. They have forced down home values and battered housing markets in many parts of the country.

The Obama administration had grand hopes for its relief effort in February 2009. At the time, officials said the government could help up to 4 million homeowners lower their mortgage payments to help avoid foreclosure.

Yet as of last month, only about 449,000 borrowers had received permanent loan modifications and are making their payments on time. That’s only 34 percent of the 1.3 million who enrolled.

The administration’s effort has been plagued by problems.

Banks weren’t prepared for the volume of calls from borrowers and were slow to process their requests for help. And the Treasury Department initially allowed banks to sign up borrowers without collecting proof of their income. In the end, many homeowners were unable to provide that information or simply gave up when the process became too bureaucratic.