Stalling and Starting issues.

My dad has a '93 Lumina 3.1 V6 that is having some serious issues. The battery, starter, and alternator are all in working condition. After you drive the car for about 10-20 minutes it just dies out and will not for the life of itself start again. If you then walk away and go back 5-6 hours later, it starts right over like there is nothing wrong.

Issues and Information:
*Car dies after 10-20 minutes of running.
*Will turn over and start after given substantial time to sit and cool down.
*When it first dies, all you get is a few clicks then nothing when turning the key.
*Give it some time, and it tries to start before the clicking ensues.
*Give it more time, and it fires right over.
*Alternator, battery, and starter have ALL passed tests.
EDIT: Update:
*NO codes on the computer, guy at Autozone just tested it.

The guy working at Autozone, which is where the car is crapped out right now, said he thinks it's a bad map sensor...

Any input from the gurus here at this website?

Welcome to AF. Has anybody checked for spark when this occurs or fuel pressure at the rail, these are the basic initial diagnostics. AZ cannot help with this, either you or a mechanic has to go through the required steps.

What you describe indeed paints a picture as addressed by Maxwedge .
However....this:
....When it first dies, all you get is a few clicks then nothing when turning the key....
..you mean all dead.?....this puzzles me somewhat...specially since you state that battery, starter, alternator are AOK....TUrn headlights ON and tell what happens when you start in conditions as described.
WHen that happens, is there any burnt smell around the ignition switch? ..faulty ignition switch leading to similar behaviour have been reported on this or parent forums. (and I have lived it myself with two previous cars..).