Spark Enigma

I have a 1970 Dart with a slant six and electronic ignition. It seems to have a strange electrical problem, when I start the car it runs for 45 seconds to a minute then shuts down, just dies, no sputtering. After 30-45 seconds of the engine shut off and the key in the off position it will start and do the same thing. If you leave the key in the on position after it dies it will not start again. It has no spark as soon just after it shuts down, I checked. I replaced the coil and ignition control module to no avail. I checked the ballast resistor and it works as well. Another point is the sooner you try to start it after it stalls the shorter the duration of run time. I'm thinking something is overheating but what? The distributor seems to have some slop in the shaft after pulling the cap and checking. Not sure where to go on this one any insight would be greatly appreciated!