Just some thoughts: Had a car once, a Pinto. I could drive it just fine for about 10-15 miles and then it would quit. Let it sit a few minutes and it would start right up and do fine for the next 10-15 miles then die. Found out there was rust floating in the fuel tank. When the car was running the fuel pump would suck the rust down until it clogged the screen. Car would die. Suction would end and the rust would float away till the next time.
A friend had a car where the coil would over heat and do that. When it cooled down, it would run again.