1990 jeep cherokee starts but when you let off the

the fuel pump runs on 2 diffierint circuts. one when the key is engaging the starter motor when you are starting the engine, and the other is to power the fuel pump after you release the key when the engine is running. there is a resistor on the drivers side on top of the inner fender that you can over ride with a jumper wire to check. if it needs to be replace its about $5.00. (its a ceramic thing about 2 inches long and bout 3/4 inches square.

I had the same problem on my jeep,it has a relay on the passenger fender well that feeds the power to the fuel pump when you relaese the key it is on a relay block with three relays it is the middle relay swap it with another relay and it should be fine