Sounds like a bad PIP sensor or a bad PCM.
Did you say the CEL will stay on and it will only start when the cel goes out?
If so I would say bad PCM with bad caps.
Why would you think it is a fuel problem?
If you think it is a fuel problem put a fuel pressure gauge on the fuel rail and see what fuel pressure you have when it quits.
Normal fuel pressure is about 32psi at idle and 40 psi at WOT.
Very unlikely to be a fuel problem as it has nothing to do with the CEL.
Very unlikely to be a ICM problem also as it has nothing to do with the CEL.