I have had the same issue on my 03 F150 4.2L. I tried cleaning the MAF sensor and the whole air intake system but the problem came back . So, I tried again, the same thing, good for a few minutes then back to the annoying gas cutting off .

and after a very long struggle,, one of my friends suggested to take it to a mechanic he knows.. and after two hours of diagnosis he connected the fuel pressure gauge and told me to drive the car with him .. and while driving the gauge appeared that the pressure of the fuel pump was so weak only about 20 psi and when I push more it disconnect . then he said that was an evidence of fuel pump defect, so when you turn the car off and turn it on the PCM reset all the ratios what makes the car work for a while but when you accelerate the pressure failed to send the amount needed .

After that, the mechanic disassemble the fuel tank all together with the fuel pump, then we got shocked when we discovered that the tank was so dirty and rusty what caused the pump to clogged and stuck.. then he washed the tank and cleaned it all together with the fuel rail and injectors and installed a new fuel pump but he suggested at any chance to change the tank because it might raise the same issue ..

All the problem was gone after that headache ...