I have a Bluetooth Microsoft Surface Mouse and Microsoft Bluetooth keyboard on my Surface Pro. When I upgraded to 8.1 I started loosing the Bluetooth connection to the devices if it sits for any length of time. It does not have to go into Screensaving mode.
With the mouse in the Bluetooth menu it says it is connected but the mouse will not work. I have to either remove the device and add back on, restart the computer and most of the time if I put it in sleep it will reconnect but not always. The keyboard does the same thing but not as often. I have removed them from device manager. Checked for updates etc. I also made it so Bluetooth can't go into power down mode. This probably shouldn't affect it but I have 13gb left on my hard drive.