Why is Jimmy Valentine pardoned?

Jimmy Valentine is pardoned because he has many important friends and connections on the outside. The last sentence of the first paragraph of the story indicates this important fact.

When a man with as many friends on the outside as Jimmy Valentine had is received in the “stir” it is hardly worth while to cut his hair.

Jimmy is characterized throughout "A Retrieved Reformation" as young, intelligent, good-looking, well-dressed, and popular. Everybody, including the Warden, likes him. The name Jimmy, rather than Jim or James, is intended to suggest likeability and popularity. The last name of Valentine suggests affection. Jimmy has "many friends on the outside" because of his winning personality. Since he is very successful in his profession as a safecracker, he is generous with his money. No doubt he contributes handsomely to the right politicians in the days when graft and corruption were so commonplace.

At the same time that Jimmy is portrayed as successful, there are some indications that he may be too successful. Too many people know about him and talk about him. He seems to be in danger of becoming a hardened criminal who keeps getting arrested and spending more and more time behind bars. One indication is contained in the first words Mike Dolan, an apparent cog in a big politician machine, says to him.

“Sorry we couldn't make it sooner, Jimmy, me boy,” said Mike. “But we had that protest from Springfield to buck against, and the governor nearly balked. Feeling all right?”

Jimmy has been incarcerated much longer than he had expected. This must have given him time to think about his future.

He had served nearly ten months of a four year sentence. He had expected to stay only about three months, at the longest. 

Jimmy knows he is in danger of losing all his "friends on the outside" if he keeps getting busted for bank jobs. They will want to forget they ever knew him. He has become too successful, too notorious. When he commits three safecracking jobs right after being released from state prison:

Ben Price investigated the scenes of the robberies, and was heard to remark:

“That's Dandy Jim Valentine's autograph. He's resumed business. Look at that combination knob—jerked out as easy as pulling up a radish in wet weather. He's got the only clamps that can do it. And look how clean those tumblers were punched out! Jimmy never has to drill but one hole. Yes, I guess I want Mr. Valentine. He'll do his bit next time without any short-time or clemency foolishness.”

Jimmy is smart enough to move to an entirely new territory of operations. In Elmore, Arkansas, he falls in love at first sight with Annabel Adams and decides to reform. But she is only the catalyst. He had been sensing the need for a change since spending ten sobering months in prison. He seemed indifferent to the Warden's lecture at the time of his release, but he was really thinking along the same lines as the Warden, who liked him and gave him this sincere parting advice:

“Now, Valentine,” said the warden, “you'll go out in the morning. Brace up, and make a man of yourself. You're not a bad fellow at heart. Stop cracking safes, and live straight.”

Jimmy was beginning to realize that honesty is the best policy, that crime does not pay. A man with all his superior assets--intelligence, skills, good looks, winning personality--can do better by going straight than by following the downward path of a recidivist. His success in Elmore proves it. He is soon engaged to the most beautiful girl in town and has become a prosperous leading citizen.