Must a wife remain with her husband who used to commit sins, has repented, and asks her to help him be righteous?

The husband erred by disclosing his sins. He should conceal himself with Allah's concealment and not expose himself, based on the Prophet's (peace and blessings be upon him) saying: "Whoever commits any of these abominations, let him conceal himself with Allah's concealment." The jurists have agreed upon the desirability for a person to conceal himself if something blameworthy has occurred from him. And as long as the husband has repented and shown remorse, his repentance is hoped to be accepted, for "the one who repents from sin is like one who has no sin."