I can't explain why a broken back sensor could prevent one from entering the doors also.
I guess you learn something new everyday....
And, you are right, the rear antenna is the only one exposed to weather elements.... good luck to us all.
I have similar issues when my smartkey is in the same pocket as my IPhone. Button on door hanles won't activate if they are together. Any chance you have a similar situation with proximity of another device causing interference?