Suspect the backup battery, although the led may remain lit this is no indication of battery condition, you can light a L-E-D with a pencil and a nail pushed into a lemon, but you couldn't run your alarm on it, in other words the battery doesn't have the power required.
If the battery is over 3 years old you should replace it as a matter of course,they dont last for ever and changing the battery would be part of an annual maintenance routine.You should be aware that a faulty battery could lead to irrepairable damage to the main pcb.
They are not too expensive , under a tenner at Screwfix, so treat your system to a new lease of life, and you and your neighbours will have peace and quiet as a result .
Pete., July 2007