It certainly has nothing to do with the fob batteries.
Try a computer reset first - disconnect the negative battery cable and wait 20 minutes, reconnect.
If the 3 and out scenario still exists, then you have the dreaded SKREEM issue, meaning the SKREEM module does not like the transponder chip ( unpowered ) in the fob, or
the PTCM ( power train control module ) does not like what the SKREEM is telling it.
There is a LOT of argument on the fix for this currently, do a lot of reading here on the forum and form your own opinion and go with it.