We have central heating system run by wood with a battery back up.
The back up last for about 2 hours.
Time to let your fire die down.
Ours is 2 years old and working fine.
To check your battery , run your system on battery backup for an hour and a half, recharge for 12 hours and then run again for an hour and a half.
This will test to see if your battery is OK or needs replacing.
Used to be in electronic test before retiring here.