I own a Macbook Pro 15" mid 2015 model and have OS X El Capitan installed. Also, I use the Macbook in clam shell mode and have two 27" Apple Displays attached to it.
When I restart the computer, the login screen shows up but moving the mouse has no effect. Every time this happens I have to open up the Macbook lid and use the integrated trackpad instead to click on my login pic. Then I can use the (external) Bluetooth Magic Keyboard to enter my password.
When OS X has logged me in, the mouse suddenly starts working normally.
This is very annoying. Why does my bluetooth Magic Mouse not work on the login screen (although the Bluetooth Magic Keyboard works) but after logging in, the mouse suddenly starts working?