I had bluetooth problems as you described with my Nexus 5 and Uconnect with it dropping after the first ring. Very frustrating.
In some research on xda-developers (an android developer forum) I found some mention of some apps running the telephone service through them when a call was initiated. This caused some bluetooth devices to think the call was either lost, or handed off to another device or app and thus gives that message of call ended even though the call remains active on the handset.
I played around and uninstalled some apps and found when I uninstalled Google Voice, I never had the problem again. I re-installed all the other apps I uninstalled except Google Voice and everything continued to work fine.
There may be other apps that cause issues like this too so you may want to play around with uninstalling apps and see if any of them are causing a conflict like this.