Share your experience!
Did you try simple troubleshooting like restarting your device or switching airplane mode on then off?
I have similar issue in Xperia Z5 Compact. After update to Android 6.0 Bluetooth keeps stopping and restarting. Connection to car handsfree is first established but then phone reports that bluetooth has stopped. My car is BMW 525i 2007 model. Used to work fine before the update.
I'm sorry to hear that 
What bluetooth devices do you have connected (do you have more than one)?
Could you try if this also happens in safe mode?
I have only car handsfree connected. Tested today and same happens in safe mode.
Doesn't matter in Safe Mode either. Does the same. Other than reset to factory settings do you have any other advice?
Would it be possible for you to take a log file from your phone after it has been disconnecting/reconnecting and send it to me?
To do this:
Settings > About phone > Build number, tap 7 times on the build number
Go back and select Developer options and turn on "USB debugging"
When it's been disconnecting/reconnecting:
Settings > Developer options, select "Take bug report". When the report is ready share (may take a minute or so) you get a notification that you can tap and share to Google Drive. Please send me a link to this file in a private message.