If fuel pressure comes up at key-on, but quickly drains down, and it has a vortec motor, then fuel is leaking from the injector "spider" inside the intake. If it starts with fuel pressure normal, but looses pressure while running, change the fuel filter.
If it's a later model (late 1990's) the fuel pump relay has gone bad, can be replaced as a single part, and you don't have to repurchase the entire fuel pump assembly.
the jimmy specific problem I'm familiar with is on the 88-95 4. 3l w/ mfi. this fuel system has the fuel pressure regulator is inside of the intake manifold, it can start to leak, badly in some cases. I've also seen cracked lines inside the manifold.
The most common cause on GM vehicles is a partially obstucted fuel filter. The fuel pump pressure relief valve can also cause this problem by allowing to great a return flow. Also a fuel pump relay can cause intermittant fuel pump action causing fluctuations in pressure.
The only things that could cause a drop in fuel line pressure is either a faulty pump or a leak. Check all your fuel lines to make sure no fuel is leaking out. Also inspect the fuel pump as well as all the wiring and fuse in the fuel system.