Impatient, Ms. Ross put in applications at three other lenders, but each was rejected or left in limbo. Finally, PayPal got back to her with an explanation: Her loan in June was issued under an incorrect employer identification number. The company fixed the mistake, and Ms.

Before taking the PayPal loan in June, Ms. Ross had accepted, and then Arlington lend payday loans returned, a loan made in April by a different lender. That loan still shows up as active in the Small Business Administration’s system, making it look as if she double-dipped last year, which is forbidden.

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The process was notably erratic: Each lender he approached asked for a different set of business records

Ms. Ross has sent multiple emails to to the Small Business Administration’s customer-service address describing her quandary. After two weeks, she received a generic response instructing her to direct questions to her lender.

“It’s such a mess,” Ms. Ross said. “In my head, I’m thinking about it all the time. Are they going to run out of money? Is this ever going to get resolved?”

Matthew Coleman, an agency spokesman, declined to comment on individual cases like Ms. Ross’s. The Small Business Administration “continues to follow through with its commitment to improve resolutions of data mismatches and eligibility concerns,” he said.

In mid-February, the agency began allowing lenders to essentially override many of its error flags and self-certify the eligibility of borrowers tangled in red tape. It also has a dedicated help line for lenders, but that, too, has been overwhelmed.

“In the first round, we could call the S.B.A. and get a warm body to talk about a resolution of a matter,” said James Bason, the chief executive of TruFund Financial, a lender that focuses on underserved communities. “That’s been much harder this time.”

Many persistent borrowers have succeeded: Thien Dang finally obtained a loan for his website development business in Woodstock, Ga., after trying four lenders.

Mr. Dang got a $5,200 loan in April from a regional bank, but when he returned in January for a second-round loan, his application was stalled for weeks, for no apparent reason. He ran into similar delays at the next two lenders he tried. Finally, his fourth application, through Biz2Credit, was approved.

“It was nowhere near as fast or efficient as last year,” Mr. Dang said. “But any relief at all is helpful.”

Lenders and government officials believe the program’s funding will be enough to meet demand. The first Paycheck Protection Program notoriously ran out of funding in less than two weeks. This time, more than one month in, the program has disbursed less than half of the available money.

But the clock is ticking: Lending is scheduled to end March 31. That deadline has spooked some borrowers who fear they won’t get their problems resolved in time.

“There’s a lot of anxiety,” said Rohit Arora, the chief executive of Biz2Credit. “People are angry, upset and they’re suffering. Not knowing how long things will take is adding to their frustration.”

Through its lending subsidiary, Itria Ventures, Biz2Credit has been the program’s most active lender this year. Mr. Arora estimated that at least 20 percent of the nearly 140,000 loans the company had made ran into problems.

Nearly 70 percent of the loans approved this year have been for second-time borrowers, according to the Small Business Administration’s data. The largest share of money has gone to borrowers with food and hospitality businesses.