Well, I'm getting screwed by my insurance company, so I'm paying for the transmitter out of pocket.
Once I have my replacement in hand, we will be covering replacing the transmitter battery.
12/6: Update: Battery is still working. I think the low battery conniption the Dex throws must be coded in, and has nothing to do with the battery. Very uncool. Do the math, if the battery was so low 40 days ago, that the receiver was missing signals etc., for a week, how does it fix itself and work problem free after that? Range is still great, not like some internal setting kicked the transmitter output down to conserve battery.