[DanEC]

I would sort of doubt a fuel delivery problem if the engine is dying like the key was turned off and the car immediately starts back up. It would usually take a bit of cranking to fill a low fuel bowl. Fuel problems usually don't cause the engine to stop like turning off the key. A trashed up filter may allow you to start out fine but will cause the engine to lean out and stutter when you start to open the throttle, but not usually die completely.

That would leave electrical. I would make sure all your connections are tight at the starter, MSD box, distributor and the ignition switch and then consider trying another coil if you can find a spare.