Well to be honest with you if its not got battery back up its not a Cat 1 alarm and isnt really going to be doing much for you, being as if someone wanted to pinch the car they could just cut wiring.
Probably not the answer you're after but i'd rip it out and fit a nice Toad in there, mine cost me £113
Dont really know what else to suggest and you've tried the usual, you could try replacing the transmitter battery, you never know.