Welcome Michi:
If you've read this thread as well as others, you'll find that many T-Birds including a lot of 2005's had battery issues.
The TB batteries are unique to this car. Since they are not under the hood where there's a lot of air flow, but in the trunk, there has to be a tube that exits to the outside for any gasses that build up. Therefore I believe that Ford is the only place and your best bet for replacement.
Two points:
If still under warranty, I would call the 800 number for service every time and therefore they would eventually replace it to cut their losses.
If not under warranty, I would have a discussion your service people that says, you think there is a drain somewhere that they have not identified it. Then ask, if you buy a new battery and still have a problem, will they
search for the cause? And what are their responsibilities under the new battery warranty if it continues to drain?
Not a good situation, I agree. On another note, if you are dealing with Ford dealerships, and there is a Lincoln dealer close by, I would suggest that you switch. They seem to be better at dealing with TBird issues anyway. Why? The drivetrain for the Birds came from the Lincoln LS and there are very many of those on the road and only 68,000 of the Birds. Just a suggestion.
🙂 and I hope this helps.