Can of worms this one could be!! sounds like your fuel pump is shurring off for some reason, this could be down to a few things... faulty fuel pump itself, you would need to rig up a test lamp to the power side of the multiplug to see whether it was losing power to the pump, also this would need to be repeated on the earth side as some systems switch the earth side of the circuit.
If you are not losing power or earth then the pump would be suspect. If you are losing power or earth you would need to check the emegency fuel cut off switch and the fuel pump relay. Finally check that the E.C.U (Electrical Control Unit [computer]) is operating properly, a fault code check would show up any problems with the E.C.U.
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