Loss of power when I press the gas peddle after long periods of driving

Problem does not come up on short drives around town, but after longer periods of driving when you press on the gas peddle you have no power, engine continues to run. first I replaced the fuel filter, still had the same problem, then replace the catalytic convertor (car has 111,000 miles)Problem occured again even after the replacement of the catalytic convertor, not as severe, but is very unnerving as to how far from home can I drive. Now people are saying it could be the fuel pump, but that is so why no problems on short drives.

why no problems on short drives. Maybe it is over heating.

Engine does not appear to be overheating.
Hope I explained the problem accurately. It is like the engine is choking for fuel
Like I said so far has not happened on short trips around town.

I think Joseph is leaning toward a heat-soak problem with a sensor or module caused by elevated underhood temperatures. Maybe like the fuel pressure regulator. A fuel pressure test can help pinpoint a problem in the fuel delivery system. Otherwise, I’d also suspect dirty fuel injectors or maybe even a dirty MAF sensor.

With a fuel pressure gauge and vacuum gauge connected appropriately to the car one might indicate the cause of the problem next time it occurs.