1997 Pontiac Firebird Engine Shut Down

After driving for about 15 or 20 minutes the car's engine abruptly shuts off but still has battery power. Once that happens, it struggles to turn back on until it has cooled off about 10minutes or more depending on how many tries the key is turned. The ignition switch was burnt out and it was replaced along with the connectors but still has this problem. I've come to guess that it can be the ignition module, a relay of some sort, sensor, or fuel pump issue. I would greatly appreciate the help.