Engine dies, but turn the key off and back on it fires right back up

I'm 4 years late to this but I saw a link to this topic from a guy at FBBO.
I'm dealing with a random NO spark issue where my '70 Charger (big block, MP electronic ignition kit) will do one of the following:
Run fine all the time.
Run, then just die and have no spark...I wait a little bit and it starts up normally.
Run, then just die and have no spark...swap parts until it starts (Who knows if anything helped, the damned thing may have started with no changes)
Cold start after sitting, no spark. Warm engine after running awhile won't have spark.
No spark cold or warm engine, spray ether down carburetor and it starts up like normal.

I'm cleaning the bulkhead terminals and packing the plugs with dielectric grease tomorrow.
Not sure why you got pointed to this thread. The OP replaced the ECU and solved his problem. It sounds like you have changed the ECU?
Lets think what we need to narrow the problem down.
I assume you are checking no spark with a spark tester. On #1 or on the coil wire?
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Glance at the ammeter next time this happens. If it shows a slight discharge then the ignition is still drawing some current. If not, then the ECU or distributor pickup or connections are suspect. Its a small draw so will not move the needle much. You'll have to be the judge on that.
if that is too subtle, then use a voltmeter to check for power at the coil and at the feed for the ECU. Or better use the ammeter and a portable voltmeter.

Coils will sometimes die intermittantly, but I;m leaning against that since you can restart immediately. Do check the connections though.

Since the ECU wiring is add on, check the new and old connections.

All of the above. How was the ECU wired in?

For example, if with the key in start there's no power to coil, then work back to the key switch. If there is power there, then check power feed to the ECU.