I peronally take any engine failure as a non-normal system behaviour.
I would not restart unless I have the other one quit on me also...
You don't know, what you will get yourself into, and the few indications we have in the cockpit hardly give a way to diagnose (unless it quits with a loud bang, EGT overlimit, or the like).
It is tought differently at my company though, and for the sim sessions I recommend to do it as your instructor says you should. Make up your own mind, once it is your but in the aircraft, not the instructors...
Nic