This seems like a natural for JJ's oft recommended troubleshooting technique. A pressure guage teed in at various points, assuming they are acessible, will tell you where there is zero pressure. I would try the pump outlet first, sounds like a classic case of a suction leak.
Not that I ever did anything like this but back when diesel equipment was less sophisticated one could drive
an operator/mechanic nuts by dropping a rag in the fuel tank. Rag would find it's way to the fuel intake and either stop or lose all power. Stop engine, rag floats away from intake, engine runs normally until......
Anyway, I would pay special attention to the suction side, clear into the sump