[shorod]

Your symptoms sound pretty consistent with a weak fuel pump. The fuel pump is a DC motor with brushes that wear. Similar to a starter motor, when hot a weak/faulty motor can fail to get continuity with the commutator or through the windings. As it cools, the open circuit contracts and again makes contact, thus allowing the motor to spin again.

You could just replace the pump, but if you want to have high confidence the pump is your problem, you can attach a multimeter to the fuel pump and trigger the "Max" feature. Attach a fuel pressure guage to the fuel rail Schreader valve, then turn the key to crank the engine. If you see a Max reading of nearly battery voltage at the pump and see virtually no fuel pressure, chances are pretty good the pump is bad. This is assuming you don't have a restricted fuel filter or fuel line.

-Rod