Could be the ignition amplifier module attached to the distributor. Have you ever had any work done to this module? Original or replaced? If yours is overheating and failing, it'll shut down the ignition system. After the engine cools, it may work well enough to start and run the engine.
One way to test; next time the failure-to-start occurs, remove a spark plug, connect it to its lead, ground the plug against a good ground, have someone turn the key to start and look for a spark at the plug. If no spark, I'd be looking at replacing the module. If a good spark, then likely fuel related. If the car has just started doing this, I'd lean towards ignition rather than fuel issues.