jaguar xj8, 1998 model
I think this may be more of a "psychological" answer than a "mechanical" one. Late Wednesday night, the last time the alarm went off, I placed the key in the ignition, and rolled it to position II. I then started the car and drove it about 5 miles. When I got back home, I let it idle for about 3 minutes and then turned it off, and locked the doors via the door lock, and I haven't had a problem with the alarm since then.
The reason I think it is a "psychological" problem is because it is a "panic" alarm. If the car car has not moved I haven't done much to remove myself or the vehicle from the original situation that caused the panic. Therefore, the alarm is probably set to repeat every "X" number of minutes in the event that the driver / occupants are incapacitated.
Granted, I'm no mechanic. But that is my idea of what coccurred.