Go to the top of the class Darren, you were very close
The Clifford battery-back-up sirens use their own internal power to give arm/disarm chirps. This is to give you an idea of when the internal batteries are running out. (they use the vehicles battery power if the alarm triggers, so you can't test it that way. - If you disconnect the cars battery with the alarm armed, it should only change tone slightly, if after a few seconds it starts getting quieter, it's definatly a siren/battery problem)
Clifford don't sell the battery pack replacements, you have to get a new siren, but I would think you could probably take the siren apart and replace them yourself. They are only lithium packs like the ones cordless phones use.
Some of the Concept range have different chirp settings - Loud, soft, silent. If you've inadvertantly selected soft chirps, you'd know about it as they change pich quite a lot at the same time.