As with all people who join the military, the reasons for wanting to rejoin vary widely. Some say they want to finish what they started, but on their own terms. Others point to the steady pay, good health care and retirement benefits. Still others talk idealistically about a desire to serve and be part of an enterprise larger than themselves.

“It’s a hunger,” said Mr. Copas, who now works with homeless veterans in Knoxville, Tenn. “It doesn’t necessarily make sense. It’s the idea of faith, like an obligation to family.”

Jase Daniels was actually discharged twice. Because of a clerical error, the Navy failed to note on his records that the reason for his first discharge in 2005 was homosexuality. So the following year, when his services as a linguist were needed, the Pentagon recalled him.

“I wanted to go back so bad, I was jumping up and down,” he said. “The military was my life.”

He was open about his sexual orientation while deployed to Kuwait for a year, he says. But a profile of him in Stars and Stripes led to a new investigation, and he was discharged a second time upon coming home in 2007.

Now 29, Mr. Daniels says that in the years since, “I’ve had no direction in my life.” He wants to become an officer and learn Arabic, saying he is confident he will be accepted because he has already served as an openly gay man.

“No one cared that I was gay,” he said of his year in Kuwait. “What mattered was I did a good job.”

The issue of rank could discourage many from rejoining. Because there are fixed numbers of jobs or ratings in each of the armed services, some people might have to accept lower ranks to re-enlist. And those allowed to keep their former ranks will still find themselves lagging their onetime peers.

“I’ve been out six years, so my peers are way ahead of me in the promotion structure,” said Jarrod Chlapowski, 29, a Korean linguist who left the Army voluntarily in 2005 as a specialist because he hated keeping his sexual orientation a secret. He is now thinking about rejoining.