I have the same problem with a 2010 Ford Fusion. I have had 3 different mechanics look at it for weeks and all gave up.
I did mess around and pulled Fuse 36 for "Passive Anti-Theft Sensor (PATS) transceiver and let it set for 3 days and that worked, the started the battery was fine! The problem is the car will not start with that fuse pulled. But it does eliminate the draw, this car would not last more than 2 days, most of the time it would be completely dead overnight without that fuse pulled

 

I believe I answered this post in another post.
This problem involves the security system and not very many shops have that training or equip. A dealership is the better way to go.