on my 95 lumina there was one small pigtail hanging out by the air hose from the main bunch of wires, dangling down by the transmission. turns out that on some years, apparently, there are two systems that tell the fuel pump to give fuel: one for when the car is starting, one for when the car is running. well, the car would start and then die right away. so my mechanic friend connected this pigtail to the positive terminal and then the car would stay running (!!!).
the bad sensors that we speculated about, crank and cam position sensors, could have told the fuel pump not to work. so the car would start fine sometimes, but then when it started those sensors told it to stop giving gas. tested it a little and it worked consistently.
if you connect this, put a kill switch and fuse or something cause it will keep the pump running 24/7 and drain your battery.
sometimes when under load before i did that direct connection to the pigtail it would die too, so my mechanic friend speculated that it was a fuel pump going bad too.
i have sold the car and the new owner has replaced the starter and battery but says that it only starts when it wants to still. i'll suggest that he jump start it too, cause i got the idea that that helped me sometimes, but something else might be going bad with it too.
also, i looked on someone's 99 and didn't see this pigtail, so it may not be there on all years.
best of luck