Being retired from 37 year career trouble shooting simple & complex computer & network problems, I blew this one! (but learned a lot about the Vette). I theriorized about the odds of having 2 FOBs with weak batteries but did check one which read 3.1v.
When I saw your reply, I thought I would measure the other battery, yep 2.4v. Schazzzam. !! Replaced BOTH batteries. I guess the spare FOB that read 3.0 had just lost needed current required.
Many thanks for retuning my trouble shooting approach!!!! This was my first ‘problem’ with my 2010 Grand Sport with 25k.