Jeff:
Gee, I have not had an alarm system problem for, abt. 3 or 4 months, It just quit working and I have not had the time to try and figure it out.
Da da, NEW PROJECT :
Under alarm system comes on while driving OR Alarm intermittently arms itself.
Ground connection, terminal 2, of alarm system control module 14 pin connector is spread apart and has poor or intermittent contact.

Carefully tighten socket with pliers. Do not replace switches for this problem. Alarm control module is located in passengers footwell under floorboard.
ALSO,Trunk lock element out of adjustment causing central locking system to arm alarm system. ?????? (Maybe you should start with this one, when you use your key it sounds off, right?) Stepping on brake pedal or turning on the ignition switch sets off alarm.

Adjust trunk lock element properly..
ALL E-CLASS Alarm intermittently arm by itself.

Moister in alarm system electrical connectors in harness channels under front floor mats causes short circuits.

Clean connectors and relocate to pillar areas.
WOW.
Much talk of corrosion and moisture. Think I'll start there, bout U??
Maybe this project will drive us nuts.
Later
Den