A woman who six times failed the physical test to become an FDNY firefighter is being given another chance — and this time, critics say, the fix is in.

“She’ll graduate, no question,” said an FDNY member. “The department does­n’t want another black eye.”

Wendy Tapia was allowed to conditionally graduate from the Fire Academy on May 17, 2013, even though she had failed the running test.

After swearing her in, the FDNY gave Tapia five more chances to run the required 1.5 miles in 12 minutes or less, but she couldn’t do it. She quit — never having worked a tour of duty.

Now Tapia, 34, is getting yet another chance to join The Bravest. She’s among a group of emergency medical technicians promoted to probationary firefighters and set to start the 18-week training academy Monday.

Tapia’s return comes as the FDNY has quietly eased its standards to ­admit more women.

After paying $98 million to settle a federal lawsuit charging bias against ­minority applicants, the city is loath to face a gender-discrimination suit, sources say. Female firefighters number only 49 in the 10,500-member force.

At the end of her last Fire Academy stint in 2013, Tapia blamed her failure to pass the running test on a foot injury.

United Women Firefighters, a group of active and retired FDNY women, persuaded then-Commissioner Salvatore Cass­ano to let Tapia graduate — and pass the test later.

She was assigned to ­Engine No. 316 in East Elm­hurst, Queens, but never worked a shift.

Over the next six months, she failed the test five more times. After the sixth try, she finally ­resigned and returned to her former EMT job.

At the time, UWF president Sarinya Srisakul blamed Tapia’s running failure on stress fractures in the academy — and The Post’s coverage.

“She’s small and they overtrained her,” Srisakul told the Village Voice.

The FDNY hunted insiders it suspected of leaking information on Tapia.

Lt. Elizabeth Osgood, who objected to Tapia’s special treatment, was barred from promotion for months. Capt. Paul Mannix, the president of Merit Matters, a group opposed to quotas, was forced into silence.

Reached by phone last week, Tapia hung up on a reporter.

FDNY spokesman Jim Long refused to comment on Tapia, but said, “All who enter the academy must meet the same requirements in order to graduate.”