Engine dies and then won't start

1998 Jeep Grand Cherokee Limited 4.0L 6 cylinder, automatic, 29,000 miles, all original parts.

If the car is allowed to sit for 2 or 3 weeks, it then can be used for 2 or 3 days with no problem. However, after this time is up, the engine will just abruptly quit. Sometimes it can be started again after a few minutes, but most of the time it refuses to start until it is almost stone cold. If you can make it past this "barrier" it will run flawlessly when hot.

I believe it is a fuel problem, as it never backfires when this happens at highway speeds, and I believe it would if unburned gas-air mixtures were present in the exhaust system when it refired.

No codes, no lights, nobody can figure it out, but dealers and garages want to just start replacing things.

I would be grateful for any suggestions.