I have a 2004 TL. My house has two rolling code garage door openers. I have had success programming both doors. Link #1 is the left door and link #3 is the right door. After having the car about a month, the right door would not work with the TL's homelink #3 button. The left door works fine. I re-programmed the right door to the #3 button and it worked fine... for about 3 weeks. Now again, the right door will not work. So, (much like the seat memory buttons) the car chooses a time when it will simply not "remember" certain settings. I might add that both the remotes that came with the garage doors work fine, so it is not the individual opener. Has anyone experienced a loss of car signal like this? Does anyone know of a TSB on the homelink?
DAMN! Locked out again!

 

I've had the exact same problem you're experiencing. Left homelink works perfectly, while right one is hit or miss. I programmed right door into the middle homelink and it seems to work a little better. Sometimes it works perfectly, other times I have to be right up on the garage door. Very strange.