At first I would think these things, as more general trouble shooting ideas.
have you checked the electrics? start off with basics like checking the battery and alternator and earth points.
Another thought is the carb. Did you (before the problem started) run out of fuel? It's possible you have gotten a bit of grap in the carb/fuel system. so a flush/clean might help. I'm assuming the car is in good working order, timing and tune are both good?
Given (hypothetically) it happens only when warm, is there a problem with the chock mechanism? Perhaps the choke is staying closed which is causing the car to run rich & potentially stall. That could be something to check.
Does the car struggle or do anything else before it cut's out, or does it out of nowhere just die?
Hopefully they're a few things to think about, unfortunately it's nothing specific!
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