Pontiac Grand AM.....runs and then cuts off after 5 miles or so...?

When you say turn the key and nothing happens, do you mean it cranks normal and won't start or no start engagement?? Things off the top of my head.... check if vehicle has a master relay that controls multiple systems, such as pcm & icm, as relays send power that increase in temperture and over time a relay coil can go bad causing it to loose magnetic field when hot, also check power and grounds to pcm as temperture goes up in a wire so does resistance, a ground that is good on start up my have excessive resistance when warm causing that module to shut down. Same with a power wire pcm will not run on low voltage, a voltage drop test will shop excessive resistance or corrosion in a power wire to a module, by showing you how much voltage is being used to make it through the circuit to the module. Crank sensor would also cause a no start concern, but should set a trouble code in a obd II vehicle. Cam sensor should not cause a no start, since it is usually only used for fuel injection timing, and the pcm will revert back to a preset table in its programming and it would also set a trouble code.

something is cooling down allowing it to close the gap and run again. then it heats up , expands and loses the fire.

My guess is the crankshaft position sensor.

I think your right about the ignition module.Its got moisture between it and the coils.