The OP's issue definitely appears to be a Ford Sync problem.
I have a 2012 Ford Focus with MFT (Gen 2 version 2.11) and had this exact same problem with two different Galaxy Nexus phones.
It would work fine for a few weeks but would then refuse to stay connected as soon as I chose it as a media source. (I should note here that "audio" was selected in the bluetooth settings for SYNC).
It started working again when my MFT system crashed and "performed scheduled maintenance." Pulling the fuse for SYNC should then ideally fix the problem. Until it happens again, of course.