Hmmm. I've never seen mine go low like that unless there's a battery or alternator problem. Basically what that sensor does is tell the system when to charge, so I see it go from 12+ (healthy) up to 14.5 (charging) and back.
I'll have to get some pics. I suppose if I unplug that wire and it still does it I should assume the problem is elsewhere? The battery is brand new and the alternator is a few years old.