I've had weird connection issues once in awhile with my BT keyboard/mouse at the login screen (nothing works). I notice what causes this to happen is when plugging/unplugging certain USB things like my iPhone or iPad while in the OS. I can't get it to reproduce consistently and it doesn't happen very often.
What you should do is shut down the computer. Disconnect the power cord for 5-10 seconds, then reboot. This will fix this issue every time.