Well, I was just rolling through the forums and came across this problem, so I just had to join and add something which may be enlightening.
I used to work for a performance workshop generally building cars for the Aust Sports Sedan Championships, but sometimes, we'd get street guys looking for street mods.
Anyway, This lady came in driving an HR31 Passage with an RB20 Turbo and auto tranny, she'd been having problems with the running and she'd had the car to four mechanics with varying remedies. Some told her she'd need a new ECU, some said it was the engine, one said it could be the tranny! She was just about to spent upward of $1.5K on a repair until she brought it to us.
Her problem? She would just be driving the car around and it would suddenly die. She'd pull over and leave it for a while and it would sometimes start again, sometimes not for a long period. She would start again and drive off and before she knew it, it would die again.
I popped the hood and started the car whilst my boss started fiddling around with the wiring starting from the coil packs. It took all of 3 mins for him to kill the engine in the same way she described. Ignition would die, spark was lost, pump would continue to run.
We performed the test again and again it failed. The boss went to the shelf and pulled out some contact cleaner and sprayed the contacts it the plug entering the trigger box. The plug was replaced and tested. We couldn't stop the engine again. She called back 2 weeks later to tell us it hadn't happened again and thanks as we did not charge her anything. Remember, 4 workshops could not find the problem and they tested everything in the electrical system............well....almost everything.
Your prob sounded so similar I had to share it. May save you alot of money.
Regards