It does in fact transmist a heartbeat every 60 minutes or so.
What it could be is draining the battery by there being some sort of bulb in the switch.
But the heartbeat has nothing to do with weather the sensor switch is opened or closed, hence it is a constant battery drain, regardless of the state of the switch. right? Or it is a heartbeat only in one state?
I don't think a bulb in the doorbell switch would cause a problem since the unit is designed to work with a sensor that presents a dead short.
I think he just had a set of weak batteries. Is the issue repeatable when starting with known good batteries? Do you get longer life from other DS10As in your house?