2001 Mirage engine cuts off
 

The car will start and run fine. If I cut it off and come back to cut it on 10-15 minutes later it starts but only runs for a couple of seconds then stalls, if I bump the ignition it will continue to run but only a few seconds then it stalls again unless I keep bumping the ignition. After it sits for 45 min to an hour it will start and run for at least 1 hour or so. It has stalled after driving for couple hour of running. Help much appreciated.

It sounds like whatever part you continue to bump is failing once warmed up.
Replacing it should fix your problem.