Apple Support Discussions user "Dana Spiegel" describes the issue:
My magic mouse (with all updates properly installed and with USB Overdrive properly uninstalled) has a problem connecting and disconnecting from the computer. When I use the mouse for a few minutes, it will all of a sudden be non-responsive, and within a couple of seconds the "Connection Lost" message appears on the screen. If I wait another minute, and click the mouse button a few times, the mouse will reconnect. This happens periodically as I am using the computer.Solutions to this issue are not solid, though some users are finding temporary relief. An official fix from Apple has yet to appear. Until then, you can try the approach by ASD user "katzha":
I have discovered that if I hold the aluminum side of the Magic Mouse against the bottom front grill of the Mac Pro and click, the bluetooth connection is restored. This is working pretty reliably. Unfortunately, I have to use this trick 5 or 6 times a day, so I am probably going to go back to the Mighty Mouse.Are you having issues with the new Magic Mouse's connectivity or has it been a painless upgrade? Let us know in the comments.