I have noticed that if I get in and just crank the key right to start it'll take quite a while before it starts. If I let the pump go a couple seconds first it'll take right off. I don't know if that behavior is normal but it's fairly consistent in my '87.
A prox sensor like the CPS can be intermittent, but I'd expect it to be more reliable cold than warm.
You'll have best success in troubleshooting if you start with the basics. Battery voltage when unloaded and when cranking. The system runs most of the time on 13V more or less, but has to start on something between 8 and 10 (not sure what the operational spec is on these rigs). XJ electrical system is marginal already from what I have observed, so a weak battery or deteriorated cabling would probably make it tough to start. After working through the electrical and addressing any weaknesses there, the more complicated and expensive things can be checked. That's just hard start troubleshhoting 101 from a Jeep newbie with a fairly decent automotive background. But somebody could come along who has seen the same thing a dozen times and say it is, has been said here, a failing fuel pump, and could likely be right. A few weeks ago I did some cleanup and maintenance under the hood on my newly acquired '87 and came out of it with an idle speed of something like 2500. A quick search of the forum and post after post seemed to be saying "you fried your TPS when you hosed down the motor, dumbass", and they were dead right. That said, checking the basic stuff is still a good idea in my book
