Help! Jeep gets to operating temp then shuts off (no check engine light)

Another test you could try is to disconnect the crankshaft sensor when the engine is running and cool.I would think it should throw a check engine light and also engine should stop running.Anyone confirm unplugging will throw a CEL?
 
So I think I found the culprit! Took the cps off and the wires are cracked and melted. Looks like they were hitting the header. Getting a new one in the morning hopefully to solve the problem!
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If i understand correctly, the engine would run fine in open loop (cold) mode,
But when the engine reached normal operating temp, it enters closed loop mode, where it then starts gathering input from sensors , so when it checked the bad cps, at warm up, it shut down
 
It dies sitting or driving.
I just had to replace my 2nd cam censer in 4000 the first had a bad belt noise and then this time it was hard starting so I thought since I already changed the cam censer it was the crank censer it was hard starting like out of gas but I just filled tank run fine up to a shift point then fall on its face shift gears and it would run good up to a shift point it ended up being the cam censer
 
Were you ever able to figure out the problem? Im currently having the same issue. Jeep will start and idle fine in the driveway for about 20 minutes then it shuts off. It acts as though its starving for gas if you press the gas pedal too fast. Checked the gas pressure and it seemed fine.