Its probably safe to say in the last few years,when mains power is lost to your alarm control panel, the back up battery (before it was swapped out) would give you anything from 10 minutes to an hour backup time (dependant on the systems current demand / any alarm activations within that period...)
False economy in my eyes as it seriously degrades the security of your system
Most alarm companies measure the battery Ah capacity when the system is serviced and replace when it has lost a set percentage of its capacity (or after a set time frame 3 / 4 years)