Yes, either the battery or something with the the system is faulty. Maybe a blown fuse or something more serious.
Power cuts should never cause alarm systems to become unusable or false alarm, if they do they are unmaintained and a sound pollution nuisance to neighbours.
If your system becomes a continuous nuisance your local authority have the rights to force entry to your property and disable it then resecure, leaving you with a bill for these services in the process on your return.