Welcome to the community 
I do have some short Bluetooth connection issues once or twice an hour, or so. But only for a split second each time and never to the point that my headphones lose connectivity completely.
When you say it shuts off, are you no longer able to connect to a Bluetooth device, or can’t you even switch it back on? 
If your problem is related to hardware / firmware / drivers, switching to a different OS won’t change much necessarily. Sometimes it’s the other way round even, I’m running a custom ROM, and it took several months for a standard Bluetooth feature to get enabled again.
Maybe have a look at the discussion in this topic for things you could try.