Concerns are rising that the Federal Housing Administration could run out money if the economy doesn’t recover soon, raising the risk the agency would seek a taxpayer bailout for the first time in its 77-year history. Since the mortgage crisis erupted five years ago, the FHA has played a critical role in housing finance as private lenders retreated. It backs about a third of all new mortgages originated for home purchases, up from around 5% in 2006.