MX Master continuously unpairing itself
Without knowing what macOS version you're running, have you ensured that you have the latest version of the Logitech Control Centre installed? 

The most recent update was only released a few weeks ago. You can read more or download it from here.

If the update and info doesn't help, report back with the version of macOS you're running and the model of your Mac.

[EDIT]

Since we've established your Mac supports Bluetooth Smart technology, which the MX Master needs if connecting via Bluetooth instead of USB, I see you have three options open to you:


contact Logitech Support directly; 
connect the MX Master via USB cable instead; and,
resolve the issue preventing your upgrade to macOS Sierra. 


On the 3rd point, according to this you should be fine to upgrade to macOS Sierra if using Airwatch. Perhaps it would be worth you asking a separate question about this? You may find resolving that also resolves your MX Master issue, since you'd be able to install the latest version of the Logitech Control Centre.