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It sounds like a bad crankshaft position sensor. When they get hot, they can fail. Take a look at these links:
https://www.2carpros.com/articles/how-a-crank-shaft-angle-sensor-works
https://www.2carpros.com/articles/symptoms-of-a-bad-crankshaft-sensor
If you feel these links mirror what you are experiencing, here is a link that shows how one is replaced:
https://www.2carpros.com/articles/crankshaft-angle-sensor-replacement
Here are the directions specific to your vehicle:
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2003 Jeep Truck Liberty 2WD V6-3.7L VIN K
Procedures
Vehicle Powertrain Management Sensors and Switches - Powertrain Management Sensors and Switches - Computers and Control Systems Crankshaft Position Sensor Service and Repair Procedures
PROCEDURES
REMOVAL
Fig.8 CKP - 3.7L
pic 1
The Crankshaft Position (CKP) sensor is mounted into the right rear side of the cylinder block. It is positioned and bolted into a machined hole.
1. Raise vehicle.
2. Disconnect sensor electrical connector.
3. Remove sensor mounting bolt.
4. Carefully remove sensor from cylinder block in a rocking and twisting action.
5. Check condition of sensor O-ring.
INSTALLATION
1. Clean out machined hole in engine block.
2. Apply a small amount of engine oil to sensor O-ring.
3. Install sensor into engine block with a slight rocking and twisting action.
CAUTION: Before tightening sensor mounting bolt, be sure sensor is completely flush to cylinder block. If sensor is not flush, damage to sensor mounting tang may result.
4. Install mounting bolt and tighten to 28 Nm (21 ft. lbs.) torque.
5. Connect electrical connector to sensor.
6. Lower vehicle.
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Let me know if this helps or if you have other questions.
Joe
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Wednesday, September 25th, 2019 AT 6:27 PM