Why does my car stall after running for 20 mins.

I have a 99 Crown Vic that stalls after running for twenty minutes. Doesn't matter if it's idling or driving. I can start it back up only after it sits for 20 minutes or more. I have check and tested the fuel pump rely, fuses, battery, alternator, coolant temperature sensor and sending unit, fuel injectors and their connectors, coil connectors, and the coils which are new as are the spark plugs and boots. All have passed either a voltage test and/or an ohm test. The IAC valve is clean so is the MAF sensor. The exhaust sytem has been replaced front to back as has the DPFE sensor. The EGR valve passed its test and is clean. Now can someone lead me in the right direction as to what the problem may be.

I would like to add that the car starts up quick and easy when the engine is cold and idles beautifully. This problem did not start until my car ran completely out of gas one time. Did I possibly damage the fuel pump. I do have good fuel pressure before and after it stalls. There are also no SEC's stored and the car does not misfire or hesitate, it just shuts off. Holding my foot on the throtle does not help to keep it running either at that 20 min mark.

When I try to restart it the engine cranks fine but it acts like there is no spark. It wiil try to fire once or twice but sputters out even if I pat the gas peddle.