have you considered bypassing the alarm for the short run to make sure its not doing something screwy.
the sudden dying makes me think crankshaft sensor is bad, or wiring to it. i would check for continuity across all the sensor circuits to make sure you have good grounds, as well as voltage across the TPS from closed to WOT just for shits and giggles.
something seems goofy with the asd relay wiring situation for the random dying. have you replaced the relay and taken out all wiring from it temporarily that is not stock?
is the diverter valve good on the charger? vacuum leaks can cause weird stuff with a super charger.
hows fuel pressure?
so the ASD gives power to injectors, computer and fuel pump right?
sounds like something odd is up with your security system and its triggering that relay off.
my gut feeling is replace ASD relay and pull out the security system for now , and see what that does?
also check power and ground to the PCM
personally i would put a multimeter on everything and check for resistance.
this was interesting:
http://forums.cnet.com/7723-7811_102-248386/jeep-grand-cherokee-stalling-fixed/
how is the idle air control valve?
that could cause the thing wanting to sputter and die