My 2015 model S never showed a key fob battery warning until this year. We replaced the batteries and checked the voltage (~3.0 volts) but the problem didn't go away. Tech support guided me through two steps:
1. Reset the console display by holding down the two steering wheel thumbwheels. Wait until the display returns to normal.
2. From the Operating menu, choose Safety, then shut down the car. Wait five minutes or so then start the car in the normal way.
I followed those steps and the fob battery low warning has not returned over the past two weeks.
Three cheers for tech support!