Any diesel techs out there
I would be looking at the fuel lines themselves, sounds to me like a leak in the line allowing the pressure bleed off. It seems to be a common discussion item on the diesel forums.
Secondly would be lift pump, like AZ340 says. Lift pump feeds the high presssure injection pump at engine, and weak lift pumps kill the VP44 injection pump (injection pumps do not like to draw fuel, they want it fed to them to pressurize). Replacement VP are VERY Expensive. FASS or AIR DOG are 2 vendors that by pass the weak stock lift pump, with a dual filter / water seperator systems, to give the injection pump all the fuel it can handle.