Jeep wont start - possible electrical issue?

Hi my buddy has a stock 87 Jeep XJ, 4.0, automatic which he uses for plowing. The jeep will start fine and run for about an hour and then will suddenly stop running. I think it is electrical verses a fuel issue. When it stops running it doesn't chug like it is fuel issue and the electrical system doesn't show any drain - it flat out quits with no warning. We checked all the electrical connections to the battery, starter, altenator, plugs and rotor cap and all seem good. When the jeep dies the battery still has good power and the starter will crank strong and all the accesories work and gauge shows no drain, but it wont start. If you let it sit for 40 minutes it will then start right up again and will run for an other hour or so and will die again. It almost seems to me that something with the electrical system is heating up or is getting overloaded - could it be a selenoid/relay or something? Just wondering if anyone has any clues or has experienced this? I've run out of ideas of what this could be. We just got 12 inches of snow and we need to get the jeep running and be reliable. Thanks!

Have you tried a new coil?

At this time no we haven't - it is sitting out in the middle of a parking lot and died while we were plowing. Just happened and we were looking for advice first before we started buying random parts. Simple enough item to purchase and replace however - we can try that. Thanks for the advice.

The most common problem is the CPS, when it stops try un-pluging the CPS and plug it back in and try to start it.

I really appreciate steering me towards the CPS. I searched the forum and read the different write ups on CPS problems and they sound identicle to my problem. Got the jeep back home after sitting a while and will try working on it tomorrow when the weather gets better and I can pick up the new sensor and make sure none of the wiring was melted either around the manifold. Again thanks for sharing your knowledge on this - much appreciated!
-Todd