Hi Andrea
I was researching this as I have the same problem, to the point where I never lock the car anymore - probably not a good idea!
The following link is truly excellent (thanks for all your trouble 'Daniel Saeuberli' - & good pics too!) (but no thanks to SAAB Dealer... hurrumph!) - and all one needs to know to repair the errant alarm... BUT... you do need to be a Techie-type person to carry out such a repair. Or know of one?!
Best regards
Piers - Wiltshire, U.K.
http://home.datacomm.ch/saeuberli/files/saab_alarm_batteries.pdf
ps: this SAAB Forum has Q's & A's on SAAB alarms developing minds of their own!
http://www.saablink.net/forum/showthread.php?t=11072
Piers d'Mufette, February 2010