I would check the pressure of you fuel pump it might be getting low which would cause vapor lock. I was fleet mechanic during carburetor years and never saw vapor lock on a large fleet of vehicles until a suburban went up the mountain and the guy said it just ran out of gas until he let it sit for a while and then it started back up. I drove it around down the hill and I could not find anything wrong, so I drove it up the mountain and sure enough at around 5000' it started running out of gas. I had a bottle of cold water, and I poured it on the fuel pump, and it started right up. The mechanical fuel pump wasn't quite putting out the pressure it should, the pressure went down as I went up in altitude. This was the only time I ever saw vapor lock in my 30-years as a mechanic. I don't know if your car is perfectly stock or has been modified. Make sure all the fuel lines are running away from hot sources. You might try my water trick on the fuel pump. Also, I've had stuff plug the fuel pickup tube. It will let the vehicle run for a little bit until it plugs the tube. then I'd shut it off and it fell off the tube, and the car will start again. I had a '33 1 1/2 truck that did that. It would start at the house and get about a block. A lot of these cars' problems are because they are old, not because they need to be modified. If it ran once for years and years then there is no reason to modify anything, you just need to find the problem.
When your engine stops spray some carb cleaner in the carb and see if it runs. That will tell you if it's fuel or something else. Look down the carb and operate the linkage and see if it squirts fuel. Pull the fuel line off the carb and put it in a bottle and crank it and see if its pumping fuel. Pull the line off of the pump from the tank and blow air into the tank and see if fuel flows out of the line. At work we had spare everything on the shelves, so it was easy to throw a new fuel pump on and that usually fix it. Every once in a while, you got one that took some research. We also had the luxury of switching carbs between vehicles to see if the problem followed the carb of not. We also hooked a fuel pressure gauge between the carb and pump to see what pressure we were getting. I'll probably think of a bunch of other stuff. There were four of us mechanics, sometimes it took all of our brains to figure out the weird ones. We even had Ford dealer tuneup guy that was an excellent carb guy, he taught me "a lot". He owned '67 and a '70 Shelby GT-500 and I owned a '66 GT-350.