Possible PCM connection fault
I just worked on a 97 JGC with similiar problem and found the information here to be very useful.
The vehicle I was working on was difficult to start and would die after a few minutes. I checked the PCM connecters and found them to be poorly designed. The harness is heavy and puts a lot of strain on the connecters. I decided to try a cheap fix first. I wrapped long cable ties around the PCM and over the connecters going top to bottom. This secured the connecters and kept the harness from dragging the connecters down and causing bad connections. I don't know how well this will work yet but the vehicle I was working on seemed to run smoother, start easier and run longer. I'm unable to follow up on this possible fix as the vehicle belongs to a dealer. This may work if the PCM and the connecters are still in workable condition. Otherwise you will need to replace some parts. The reason this problem doesn't turn the service engine light on in some cases is that the loose connections may be cutting power to the PCM as if the key was turned off. I hope this works and saves you some money and aggravation. Be sure to use good quality cable ties at least 1/4" wide and pull then tight. Good Luck