I am having the same issue.
It is connecting and disconnecting repeatedly, and it is SUPER annoying because it essentially renders my pebble watch useless.
For a while i was using the Automatic Link (car link) and was getting 'bluetooth share has stopped' errors, but found that when I stopped using the Automatic app it helped a little bit (stopped giving me the 'share has stopped' error), but it still connects and disconnects repeatedly.
The weirdest thing about this is that when I first got this phone I wasn't having this problem, everything was working fine for the first month or so, but it seems to keep getting worse.
I have tried wiping cache, dalvik, fixing permissions, etc. and have not had any luck, but I don't want to do a complete wipe of all my data and lose my text messages, etc. unless ABSOLUTELY NECESSARY, since there are images and things in there that I continually refer to for work, and I have not found that titanium backup restores them very reliably.
Has anybody had any luck with this issue? Could it be a defective device? It seems to me like it should be a software problem because it is not something I was having problems with from the start...
I am very frustrated with this, even more so because I love this phone so much. I have never had a phone that I liked as much as this one, usually the first thing I do is install an AOSP rom, but I even like Sense 6 in some ways. With Nova Launcher's 'OK Google' hotword support this phone is a dream come true... if only the bluetooth worked.