There could be many possibilities, and I just went through this scenario with a friend's car. We started with checking for crap clogging the filters. Nope. We then swapped the carburetor with two others, and all three did the same thing, so it wasn't that. Then we tried the spark. It was good when we checked it, and then no spark at all when the car died. We thought it was the coil. Well, we went back and forth with coils and for a while it looked like the coil was the problem, but then with a swapped coil, it did the same thing.
It all turned out to be crappy crimped on repo flag connectors on the ends of his wires going from the terminal block to the ammeter and back and to the coil. All three of his wires had crappy crimped-on connectors that I could easily twirl around the wire with my fingers. One fell off while I had it in my hand.
We cleaned up and soldered the connectors and it ran like a champ.
Car had been sitting where it was moist. As far as I could tell, the connector(s) got some high resistance corrosion at the points of the lousy crimps. and would conduct for a minute or when the wires were wiggled from messing around with swapping out this and that, but would soon just not be able to handle the relatively small current flow of just running the engine.
My story, and I ani't changing it.