Sounds like something is heating up and shorting out or a sensor loosing its signal completely when it heats up.
The crankshaft position sensor is notorious for complete loss of signal as it heats up during the engine warm up cycle, and most times it never sets a DTC.
I known you said you have already replaced the CPS, but there is always a possibility that that it is a bad one right out of the box. It happens!
If it were mine, I would try another crankshaft position sensor and a new camshaft position sensor.
If you can get your hands on a scope like a PicoScope Automotive oscilloscope, you could monitor and test the signals for different sensors to find which one is failing as it heats up.
As far as I know, the MAP sensor will not totally stop the engine from running, if bad it just makes the engine run poorly.
There are some other sensors that are vital to engine operation such as fuel rail pressure signal, Fuel Quality Sensor on the CP3 injection pump, etc...but there has not been any reports of these failing due to engine warmup cycle that I know of.
Where are you located, you don't have a signature?
Adding a signature, location, vehicle information, etc... to your profile can help others when trying to answer your questions or simply providing advice.
To add a signature, click on "User Control Panel", then "Profile", then "Edit Signature" where you can add your information. 
See picture below.
If you have not read Sam's CRD Noob Guide, please do so as there is a lot of very useful information contained in it and it will help educate you about this unique little diesel engine.
Factory Service Manuals are available for viewing and / or downloading at:> http://www.colorado4wheel.com/manuals/Jeep/KJ/
|
