Lebaron fuel pressure problem

Hello all. I have a frustrating problem with the wife's 1990 Lebaron convertible. The car sat for about 7 years while I avoided working on it, now we want to drive it but I keep randomly losing fuel pressure. It sounds like the fuel pump is running, although maybe not the best. This is the second pump i've tried. Also replaced the filter and rubber lines. The car will run ok for a while, then suddenly the pressure drops to about 10psi. Can someone tell me what the little diaphram on the pump does and could that be my problem? and yes the gas is kinda nasty, but not the worst i've seen. Hopefully someone has seen this problem before. Thanks for helping!