Burglar alarms are generally reliable but if the internal battery is flat and will no longer hold charge it should be replaced as soon as possible.
A flat internal battery can mean that if there is a power cut the external siren will sound because the hold off circuit to it is no longer present. If the outside siren does not have a self contained battery (scb) the alarm can still go into tamper mode and activate when the power is supplied to the alarm system ( this is why many burglar alarms sound after a power cut). This video shows how to replace the back up battery.
View video : http://www.youtube.com/watch?v=4vsC9jgkVbo