Jane, I don't remember reading what type of alarm you have. If it is the datatool model made especially for our bike ie plug and play, then they don't draw hardly any power. At least mine doesn't.
If it is one of those alarms that can be adapted to any bike, well I can't comment. It may be a combination of several factors why you are getting so much grief but as has been mentioned, you probably will have to disconnect the alarm in the first instance and maybe even buy another battery and start again. Then if you have the same issue occur, you know it wasn't the alarm. Sounds like from your testing it is the culprit though.
If you still want an alarm, the datatool hasn't given me one ounce of grief in 4 years. I love mine but I was lucky to pick it up new off ebay for $170AUD. Otherwise I wouldn't have one either. This was just an offer too good to refuse.
Good luck
