Any update here? I think I have the exact same issue.
In short: When radio is operating, it will intermittently "shut off". Better said, there is no sound, although you can still see the station it is on (or the time, depending on what is selected). So you know that the unit has power, but it is not working.
Here is my saga: I have a 97 Cherokee Sport. When I bought the vehicle it had an aftermarket (JVC) stereo in it that worked fine. about two years ago, it started cutting out when the I turned the volume up high. Turning it down seemed to fix it. Fast forward to a few months ago, and it started cutting out at all volumes. As time went on, it started happening more and more. I wondered if there was an issue with the grounding, but since it goes into that spinal column of a harness, it was impossible to trace the wire back. So, I ran a separate ground from the frame under the door directly to the ground wire on the radio. No change, so I determined the ground is fine and went back to original connection. I also checked the fuse and it is fine. One night, I noticed that when it was not working, I did see two dim lights on the unit, so that told me it was getting power.
Today, I saw a stock stereo from a 99 (I think) on craigslist for $15 so i called and bought it. The 20 year old kid that sold it to me said it worked fine and he took it out two weeks ago when he bought an aftermarket unit. I put it in my Cherokee and it immediately worked, but intermittently! Same issue as I was driving home: Worked fine for a while, then cuts out, either for a few seconds or longer, sometimes many minutes at a time. Again, when it is not "working", I can still see the time/station display.
An added twist: With the stock radio in there, when it started working again, it is stuck on the same volume (about 4 out of 10). No matter where I turn the dial, the volume is that same level. Also, none of the other adjustments work (bass, treble, balance, fade)
Being that I am having the same issue with two different radios, one stock and the other an aftermarket, I am led to believe there are issues in the "spinal cord" wiring harness that disappears into the dash.
For the record, this Cherokee has over 200k miles and getting along on the rust. Also having intermittent power window issues and the rear wiper is not working. Assume the rear wiper motor is gone, but not sure
With all the Cherokee Sport owners out there, I have got to believe that others have had this radio issue and SOMEBODY must have figured it out by now. Anyone?