The Blue Light Anomaly

We have this very strange occurrence concerning our electric toothbrush.  After weeks of being plugged in to a proper 30/50 amp service,  the blue light goes out and the battery discharges.  It has become our signal that it is time to leave because as soon as we unplug and are running on the inverter, the blue light returns and the toothbrush happily does its thing.  Howard, the engineer, finds this very disturbing and pulls out all his electrical testers.  The voltage coming from the inverter is the same as the AC current.  The sine wave is true.  So in lieu of an explanation we have decided to follow it's lead and head out on the road again!