You didn't say what model, year, or engine type your Jeep has. That info would probably help.

You said you replaced the crankshaft sensor, but then you asked about the "pick-up on the flywheel". Aren't they the same thing(assuming you have a 96 Grand Cherokee)?

Do you get spark during this cooldown period?

Based on the info provided, I would suspect electronic overheating. Try leaving the PCM cover off with a fan blowing directly over it and see if the jeep still cuts out.

Put a wet wrag on the coil and see if the jeep runs until the wrag dries out. If so, it is the coil.