Is it carb or FI? Have you checked the fuel pressure after it shuts off? I had that issue on my old 1988 Mustang when the fuel pump was going bad. It would just shut off periodically and I would have to wait for a while (30-90 minutes) before it would fire again.
On your ignition cylinder issue, it sounds like something broke inside of it. I would just buy a new one as they are only about $20 for your Jeep.
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