My problem was finally resolved after a big surprise.I
I have other items that use the CR2032 battery so bought the 4-pack a while ago and replaced the battery in my primary keyfob. The message didn't go away so I followed all the procedues in forums / videos including MCU reset using both scroll wheels, reseting driver's display with buttons above scroll wheels, and simultaneously pressing top of both key fobs, etc. Low battery message wouldn't disappear.
One of my batteries measured 3.023v and other 2.975v which appears close enough for a 3 volt battery. Of course these values are at no-load and could fall when a button is pressed.
Frustrsted, I read the specs of different batteries brands and some listed 3.3v as nominal. Could a few hundred millivolts be the answer?
I installed a pair of fresh 3.3v batteries and brought both keyfobs to to the model S. Instantly, the warning message disappeared. Problem solved.
Lesson learned, don't buy multi-pack batteries for Tesla keyfobs as they are very sensitive to slightly low voltage. When the warning message appears install a fresh new battery. Batteries, although not used, lose voltage sitting on the shelf and Tesla's are very sensitive to low voltage.