Fuel pressure

I would suspect heat in the fuel the pump causing the fuel to boil and the pump gets into a partially air-locked state; it is a sort of vapor lock state inside the pump. OP, does this pressure drop when hot or does it do this when cold? (Not expecting an answer after all this time, but what the hey...)

I have experienced this good-pressure-then-low-pressure symptom happen on certain small aricraft when the old AC style mechanical fuel pump is exposed to too much heat; the cure is to put a cooling shroud around the pump and route cool air to it in those applications.