I have a Jabra Move bluetooth headset and a bluetooth Apple Magic Keyboard circa 2010/2011.
I can pair them both with my 2015 Mac Book Pro (running OS X Sierra) with ease. However, as soon as I start playing audio through my Mac to the headphones one or both of two things happens:
1) The music drops in and out
2) The keyboard disconnects and reconnects frequently.
It's so frustrating that I mainly disconnect my headphones from my mac and stream music through from my phone.
I used to have the same setup with a ~2013 Mac Mini and had exactly the same problem.
I am in a busy office full of computers, phones and bluetooth and wireless devices.