A Bronx high-school teacher who was accused of sleeping with an underage student two decades ago but remained in the classroom because of a broken disciplinary system was busted again yesterday — this time for allegedly molesting a relative.

Thomas Gibbons, 59, a special-education teacher at JFK HS, was arrested at his Eastchester home Wednesday night and sent to Paterson, NJ — where he allegedly sexually abused a 9-year-old relative two years ago.

His arrest comes just days after city officials launched a massive campaign to give the schools chancellor the power to fire such teachers — in the wake of dozens of similar cases.

By state law, the power to discipline teachers rests with an independent arbitrator — like the one who returned Gibbons to the classroom in 1996 despite accusations that he had a sexual fling with a student at the former William Taft HS in The Bronx that began when she was 15.

Both the Department of Education and the teachers union must jointly agree on an arbitrator. City officials argue the system is broken because often arbitrators don’t want to rule against teachers for fear of not getting additional work.

Gibbons was arrested in 1995 after he allegedly grabbed his student lover by her hair, slammed her against a locker and later pointed a gun at her chest.

After Gibbons’ arrest, a schools investigator tapped the girl’s phone calls and caught the teacher detailing the couple’s long alleged sex life.

He also was recorded begging her not to press charges — and she eventually agreed.

By the time the case went before independent arbitrator Margaret Leibowitz, the girl was 20 and she refused to testify.

Leibowitz dismissed the charges even after she heard the recording.

Investigators had also presented her an additional complaint by another Taft student who had accused Gibbons of touching her sexually.

“In my view, the evidence presented is insufficient to prove that [Gibbons] had sex with her when she was a high-school teenager,” Leibowitz wrote.

In the recent case, Gibbons was charged with one count of endangering the welfare of a child and faces a maximum of up to five years behind bars if found guilty.

According to prosecutors, Gibbons would periodically visit relatives in Paterson, where he allegedly abused the little girl between January 2010 and January 2011.

His wife, Kelly Gibbons, was stunned Wednesday night when he was arrested. She is Chinese, speaks little English and was due to give birth Thursday.

“She’s is not fully aware of what’s going on,” said Marie Petrie, 65, a neighbor and close friend of the couple.

“She thinks it’s lies.”

Additional reporting by Yoav Gonen and Georgett Roberts