On Thursday night's episode Michael tries to commit suicide, once in a car wreck and once by a handgun. But both times were unsuccessful. Why do you think he's able to kill other people (Libby & Anna Lucia) but not himself?

When you're on the island he's able to kill, but once you're off the island you're not. See what happened to Jack when was trying to committ suicide in his flash forward? The island won't let you.