Alarm systems need regular maintenance to avoid issues like this, SLA batteries have an expected life of 4 years for good quality ones.
I would suggest you have the system serviced by the installer.
Alternatively if you are feeling competent to DIY, it would be sensible to check the voltage and charging rate with a multimeter, when you replace the battery otherwise you will be back up there again next power cut.
It is up to you if you want to isolate the mains before opening the cover, most engineers would not but they would also be unlikely to poke there fingers near the mains terminals.