This kind of problem just about has to be something electrical. Start the car, tug on wires, twist the harness, tap on the coil with the handle of a hammer, wiggle the ignition secondary conductors, jiggle the ignition key. You can even use a hairdryer to heat up things like the coil, which might be going open at some elevated temperature.
In my Bugeye, the guy who did the restoration used the wrong screw-in cap on the coil. This left the secondary wire loose, and occasionally I'd get spells of really bad running because of it. I suppose it could have killed the engine, too, if the situation were a little worse.
It's also easy to bump the ignition key, as I've discovered, on a shift into third, and the car shuts down really fast when I do that. First time it happened, I had no idea why it stalled.
By the way, don't automatically assume it's something mysterious. A lot of these problems are simple, and if you decide at the outset it's gonna be a difficult fix, it will be. You'll probably kick yourself when you find it. I know from experience, and my well dented tush bears witness.
In short, there are an unlimited number of things that can do this. But almost all are electrical.