“It is taking an extraordinarily long time to get the refunds, much longer than we would have anticipated,” said Jeff Martin, a tax partner at accounting firm Grant Thornton LLP. “If you are looking at cash-strapped employers,” he added, “it can be pretty detrimental.”

Employee-retention tax credits were among a series of policies Congress passed in 2020 and 2021 to help businesses and workers weather the impacts of the virus on the economy. The federal government offered that aid to combat the immediate shock of closures two years ago and the lingering effects during the uneven recovery.

Congress aimed the credit at employers that faced mandatory closures or suffered steep revenue losses. But its structure is causing problems for companies. Because those wages subsidized with credits aren’t deductible from income taxes as a normal business expense, some companies are temporarily paying higher income-tax bills while they wait for refunds, Mr. Martin said.

Common Bond Bakery Bistro Brasserie, which has about 380 employees and 11 locations in the Houston area, received a $700,000 tax credit for 2021. On Nov. 1, it filed an amended tax return after an accounting firm determined that the company’s reduced head count qualified it for a $170,000 credit for 2020. Common Bond already paid the accountant $17,000 for its work, but still hasn’t received the refund.

“We are just praying every day that the money comes in,” said Chief Executive George Joseph, who plans to use the refund to pay off debt, fix equipment and provide raises. “I understand they are really backed up. It’s a tragedy they can’t release the money.”

The processing delays are an example of how the IRS paperwork backlog creates challenges for taxpayers. The agency’s struggles have also left millions of individuals waiting for 2020 refunds and slowed their ability to get answers from the government.

The delays cost the government, too. The IRS paid $55.5 million in interest on slow refunds from amended employment-tax returns from August 2020 to August 2021, according to an inspector general’s report that projected more such costs ahead.

IRS officials have said they are working through filings as quickly as possible, and they announced a burst of hiring and other changes to accelerate that work and bring backlogs to normal levels by year-end. At a recent House hearing, IRS Commissioner

Charles Rettig

said the agency was unable to automate systems to expedite these refund requests. These problems—and other customer-service issues—stem from a lack of resources for the agency, said Senate Finance Chairman

Ron Wyden

(D., Ore.).

The Aureus Group, owner of three auto repair shops in the Philadelphia area, filed its first request for an employee-retention credit last May. The 25-person business received a partial $180,000 refund this month, but is still waiting for more for both 2020 and 2021.

Aureus plans to pay off credit-card bills and other debt it incurred to keep operations afloat during the pandemic, when business dropped as much as 50%, said Chief Executive Thomas Bemiller. One location shuttered for eight months after being flooded by rains related to Hurricane Isaias in 2020, adding to financial pressures.

“When the money showed up, it was a little bit of a surprise,” Mr. Bemiller said. “Because it took so long, I wasn’t waiting on it every day.”

Congress created the employee-retention tax credit in 2020 as a companion to the Paycheck Protection Program, which provided forgivable loans to employers meeting certain requirements. The idea of the credit: reward employers who keep workers attached to their jobs.

Smaller employers could get the credit—worth up to half of wages in 2020 and 70% in 2021—for paying active workers, while larger firms generally got it only for paying people who didn’t work.

Chipotle Mexican Grill Inc.

received $11.4 million during 2021 and

Spirit Airlines Inc.

qualified for more than $37 million last year, according to securities filings.

Congress expanded the program for 2021. Employers could get up to $7,000 per employee per quarter, instead of a $5,000 annual maximum in 2020. To qualify in 2021, employers generally had to show revenue in a given quarter was at least 20% below 2019 levels, instead of a 50% drop in 2020. Originally, employers who received PPP loans couldn’t get the credit; ultimately, they could, but just not for the same expenses.

Many employers initially weren’t sure they qualified. So they filed amended tax returns, which typically must be submitted on paper, to claim the credit. As of March 23, the IRS had 1.9 million quarterly employment tax returns to process, plus another 324,000 amended returns. Not all claim the credit, but many do.

“For some taxpayers, it’s been a real bear,” said Jim Donovan, a Minneapolis-based partner at accounting firm Eide Bailly LLP. “I have taxpayers that are like: ‘Gosh, Jim, I needed the money five months ago. I need it right now. When’s it going to come in? I’m having trouble making payroll.’” For others, Mr. Donovan said, the money is icing on the cake, cash they can claim because they qualify.

Meanwhile, claims continue increasing as business owners realize they are eligible or respond to pitches from consulting and accounting firms who check eligibility and help employers claim the credit for a fee.

“We continue to get a decent amount of volume,” said

Frank Fiorille,

vice president of payroll processor

Paychex Inc.,

which has processed more than $7 billion in requests for the credit. “It can be close to a hundred a day.” The average credit for Paychex customers is $170,000, he said.

Paychex charges small businesses owners a flat fee averaging about $4,000, Mr. Fiorille said. Some firms charge 10% or more of expected refunds, business owners say.

Congress initially intended the credit to run through 2021, but terminated it a quarter early to save $8.2 billion that helped pay for the bipartisan infrastructure law. When President Biden signed that legislation Nov. 15, the credit was repealed as of Sept. 30, yanking the benefit away from employers that had expected it.

A bipartisan group of lawmakers is seeking a retroactive revival of the credit for the fourth quarter of 2021, pointing to the instability caused by its removal.

“Promises made should be promises kept,” said Rep. Carol Miller (R., W.Va.).

That effort is increasingly unlikely to succeed as the fourth quarter gets further away, congressional aides said.

The North Carolina Symphony now probably won’t get the $539,000 it had expected that quarter. Still, the group has received about $2 million from the employee tax credit and $5 million in other federal assistance. Those infusions helped fill an $11 million drop in operating income and let the orchestra keep musicians on the payroll and begin reversing pay cuts, said Rob Schiller, the symphony’s senior vice president and chief financial officer.

“We’re grateful, as you might imagine, for every penny,” he said. “They’ve really helped save the industry.”

Write to Richard Rubin at richard.rubin@wsj.com and Ruth Simon at ruth.simon@wsj.com