Well here is my story and I am stickin to it.
I got my car (Factory Stock)because the guy who owned it gave up on it after he let it sit for 5 years. He had it 15 years. This is what it did. Fires right up cold drive 20 Min... and it dies... try to re-start and just a click... wait 1 hour and fires right up... drive 20 min and it dies.
First the Battery was Small and the terminals were oxidized.
Second The Fuel Tank had so much crap in it. After it pluged it would backwash itself clean enough to run 20 min more. A new fuel filter would plug in 20-30 more min.
The Gas Tank Rust after swishing around would get sucked into the fuel filter which would clog the flow of fuel to the carb... shut down the engine and the battery had no kick to turn it over. I confirmed the junk in the tank by once the engine was cold I filled the carb with gas took off the fuel line and checked the flow in a clear plastic container. Ugly gas came out oh and it was new gas.
So a New 1100 CCA Battery bought and all connections cleaned. Drain the fuel tank with the bottom plug I stuck my finger in the opening and felt 1/2 inch of muck... So... Gut the Fuel tank and boil it was the start of #6656 ten years ago for me.
(Today, It is getting repainted it is being restored it is in primer last week block sanding this week and I am going to MSD 6al but I want to keep the points just in case)
Now you have read my story try this get a spark tester (in line viewing window type)put it were you can see it and a can of air to freeze stuff.
Run the car with no Air Cleaner on it.. in the driveway.. and watch and wait... when it dies does the spark go away or do you have no squirt of fuel in the carb.
Pray for the Spark or else you pull the engine to get the gas tank out and make friends with a guy in a radiator shop
. If it is Spark most likely it has to do with heat so hit each of the components one at a time and try to restart it. Which ever starts it again is the problem. Good luck