It sounds like vapor lock but isn’t
I have a 1980 Fiat Spider 2000. The engine is carbureted and the car has an automatic transmission. Everything on the engine is stock. I purchased the car some months ago and have found the following problem: The car drives beautifully...most of the time. When the engine is cold it starts right up every time. I can drive as far as I want with no problems. When I turn the car off and re-start it within minutes it starts right up and off I go. If I wait 20-25 minutes, it starts but will die within driving 50 yards like it ran out of gas. After about the third stall out it’s fine again. Last Saturday, it would not restart and stay running. It started and stalled immediately and AAA helped me home. Four hours later she started right up and I went for a nice drive. I know, it sounds like vapor lock. Fiats are not known for vapor lock, plus I have an electric fuel pump in the trunk and yes, I can hear it run.
My uncle bought a Fiat Spider new and my father, the family mechanic, was decisively less than thrilled. The Fiat was far less reliable and more difficult to work on than my uncle’s Pontiac that it replaced. My uncle was sometimes heard to say that the second happiest car experience he had was buying that Fiat and the first happiest was selling it.
In reality, however, he loved the car and only sold it when his first child came along. I loved it too, as it was the first manual gearbox car anyone was kind (and perhaps, foolish) enough to let me drive.
Your problem sounds kind of like vapor lock, but not quite. Vapor lock will normally inhibit the engine from restarting within minutes after it is shut off, and it will normally re-start if left to cool off for 25 minutes. And vapor lock is normally alleviated by a reasonably powerful electric fuel pump, the pressure and tenacity of which overcomes the vapor barrier.
I suspect, therefore, that your problem may be electrical and not fuel related. Inspect the ignition system for any signs of trouble. If you find any oil under the distributor cap replace the distributor’s lower seal. Look especially close at the ignition pickup and its wires. These wires often get brittle and when the insulation deteriorates you may get intermittent short circuits. If you replace the pickup take care not to crush its wires under the cap, and be sure to adjust for the correct gap between the pickup and reluctor.