Q: My mouse looses its bluetooth connection constantly.

I'm having the same trouble with my '11 iMac. Only both the keyboard and trackpad are shutting off.

I've experienced a similar problem.  The mouse doesn't automatically connect on restart, and looses connection. I have tried all the fixes I could research: remove the battery until it resets, delete the profile from the bluetooth menu, delete the preferences in both the main and user libraries, rebuild permissions in Disk Utility, and reset the pram (command-option-p-r while restarting before getting the start-up chime. There is another start-up reset command beyond pram, but I don't remember what it is.

The one constant was that it's identity from when it was used on another computer (which it never worked properly on either) would not reset to the current computer it was being used on.

If none of the fixes above work, your mouse is probably defective.

Just talked to an Apple representative. Another option is to turn off the mouse and the computer, be ready to switch the mouse back on, turn the computer back on, wait untill you see the spinning gear appear right after the Apple logo shows up, turn the mouse back on as soon as you see the gear appear.  Appearently its a timing thing. Let the computer acknowledge the mouse. Can't say if that's the solution yet, but I'll repost after a couple of days.