How many times per turn can a thief steal?
There's no limit on attempts per turn, but you do have to discard a card to attempt it, so you can't just attempt forever. From the FAQ:

Q. How often can a Thief steal?
A. As long as he has cards to discard.
Q. What happens to a Level 1 Thief who fails an attempt to steal? Does he die?
A. Nothing happens to him. You can't go below Level 1. (Beware the Level 1 Thief – he literally has nothing to lose!)