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My 1987 F150 V6 does fine with gradual accelleration. And I can rev the engine with no proglem in nuetral. BUT...when the truck is taxed in any way - for example climbing a hill - as I apply more accellerator the engine starts acting like it wants to stall out.
I have changed the plugs, plug wires, and run some fuel injector cleaner through the tank and it still acts the same way.
I'm guessing you have a 4.9 I6, because there was no V6 option for these trucks.
Has the check engine light come on? Have you tried to pull diagnostic codes from the computer? This is where you need to start. http://www.fordfuelinjection.com/?p=13
I had the same problem with Chrysler van (sorry) that I had. It would idle great but any type of load on the engine it would start to stumble. Eventually it would only idle and would die when it was put in gear. Check the fuel pump. Your truck should have a low pressure in the tank and a high pressure on the frame rail. My guess would be the one in the tank. If it is only supplying a limited amount of fuel it would not matter how hard the high pressure pump tries there would not be enough to run under load. Just a thought.
Let your old filter dry out and then check for restriction. It is common for these filters to restrict fuel flow when moisture collects in them. If filter is no longer restricted, keep it as a back up in case problem happens again when on the road.