Ok first of all the engine just quitting for no reason and then starting up again could be a fuel issue...I had this on my Export 2002 2.5 CRD on a long trip....would cut out and grind to a halt. Start it up again and would carry on for a few miles then cut out again....got worse as the trip went on.
Got to my destination and had the fuel filter replaced with new Mopar filter...no more problems.
The Red LED for the SKIS system coming on and staying ON solidly means that the ECM was happy with the SKIS code sent to it...the ECM...by the SKIM module that sits on top of the steering column.
This SKIM module has a wire "loop" going around the ignition key entry and reads the chipped code off the chip imbedded in the ignition key.
As the ECM is happy with the code received it energizes the ASD relay inside the fuse/relay box under the hood and all should work well.
When the ASD relay is energized it sends back a signal to the ECM that the ASD relay has indeed energized. If the ECM does not receive this signal it lights up the Red LED solidly. Engine usually turns over but will not fire....strange that your engine does not turn over.
I had this above sceneria on my CRD. I could remove the ASD relay and jumper female pins 30 and 87 inside the empty relay socket together and the Jeep would fire up and run until I could find time to trace the problem. This turned out to be a broken wire going to the ASD Relay coil preventing the ASD relay from energizing. Note that jumpering 30 to 87 will not let you Hot-wire the Jeep...the ECM has other ways of stopping the Jeep from firing.
What you should most definitely do is the following:
The LHD 2006 CRD has a known problem that the Fuel Filter Mounting Bracket damages the wire harness going behind it causing the wires there to fray to chassis or to other wires and causing all sorts of problems. You need to remove this bracket and inspect the wires in that area for damage.
The fact that re-plugging the ECM connectors fixes the problem for a while could be due to the above problem....shifting the harness slightly removes the short for a while...or you have burnt contacts on the ECM connectors. You can get contact cleaner to spray both sides of the connectors.