Once Souvenir Snatcher has snatched a noncreature artifact, you’ll continue to control that artifact if it becomes an artifact creature.

The control-change effect of Souvenir Snatcher lasts indefinitely. It doesn’t wear off during the cleanup step, and it doesn’t expire if Souvenir Snatcher leaves the battlefield. In a multiplayer game, it does expire if you leave the game. If the artifact’s owner leaves the game, that artifact leaves with them.