This happens occasionally when the computer is in use.
When this happens, both the bluetooth indicator in the wingpanel and in the bluetooth section of settings seem to hang until I execute the following in the shell.
$ rfkill block bluetooth && rfkill unblock bluetooth
This momentary blocking will release the UI and it will either resume the connection to the mouse automatically, or be in the Bluetooth off state which can be switched back on and be used normally.
Does anyone have any idea why this happens and is there a known way to solve this?