The next time the car stalls, try these tests:
- Check for fuel at the carburetor. Remove the air cleaner and turn the throttle lever. Fuel should be squirted into the carb. If so, move to the next test. If there's no fuel at the carb, then the car is vapor locking. Today's fuels have a much lower volatility and vaporize at a lower temperature. Sources of vapor lock are a weak fuel pump, weak carburetor accelerator pump, and the obvious - poor gasoline quality. In addition, as previously mentioned, a stuck heat riser will allow the intake to get too warm, allowing for vapor lock.
- Pull a spark plug and check for spark by cranking the engine with the plug laying on the head and attached to the plug wire. If no spark, the you may either have points that are improperly set, or a coil that's failing when hot. My 54 did the same thing...quit once warm but would run once cooled off...and it turned out to be a faulty coil.