From the service manual:VEHICLE RELOCKING

In order to avoid unlocking the vehicle unintentionally, the vehicle is relocked by the CLP/SSM via the SKREEM module. Relocking is accomplished after unlocking with the remote control when: a door is not opened within 40 seconds, the key is not inserted into the ignition lock, or the interior power door lock switch is not actuated. The CLP/SSM reads the signals (door contacts, interior power door lock switch) and actuates the power door lock actua- tors. The vehicle security alarm is also activated by the relocking function.

If the service manual is correct; The OP needs to replace the CLP/SSM in the rear of the car. Or he has a problem within the SKREEM. I certainly would replace the CLP/SSM before messing with the SKREEM. I also am assuming all the related fuses (25 & 26 particularly) have been checked and are okay.

Another way to try an isolate of the problem to the CLP/SSM would be to exchange a BCM with another similar Crossfire, Perhaps the OP knows someone who is willing to make a temporary exchange just to test the BCM.

If the little light is not blinking on the tow-away disabling switch the anti theft alarm is not resetting, and that, to me, would also indicate a problem with the CLP/SSM vice the BCM.