The previous version of Apple's Magic Mouse loses Bluetooth connection's caused by frequent battery changes and using different types of double A batteries.
You can opt to replace your mouse with the newer version that is self-contained and powered off a USB connector to recharge the mouse, or slip a small piece of paper folded to snug the batteries in the cradle.
Picking up the mouse, or sudden movements will no longer cause the mouse to lose connection with this fix, and it won't be noticeable from the outside.
You will quit replacing batteries before they need replacement at the same time because your mouse will continue to work properly with this fix.
Apparently, Apple discovered the issue, and their answer is the new Apple Magic Mouse that features a self-contained rechargeable battery through your USB ports on your computer.
Magic Mouse and Wireless Keyboard get self-contained batteries
The Magic Mouse isn't the only Apple accessory to receive the self-contained rechargeable battery. The Apple Wireless Keyboard no longer uses Double-A cells and is recharged using the USB connection.
Ultimately the best choice for solving the loss of connectivity problem is purchasing the new Apple Magic Mouse and Wireless Keyboard that no longer require external batteries, and sell your old gear on Craigslist or eBay. You'll get a high price for your mouse and keyboard, and the money you'll save on batteries will quickly make up the difference for your new models.
Besides, the best part about getting the new Apple Magic Mouse and Wireless Keyboard is how long the charge lasts in both units. I use them non-stop all day long and after several months have only had to recharge them once! That's incredible as I replaced batteries once a week, before the new gear.
Watch for other helpful tips and tricks on my blog as I post about fixes and cool new things that I think you may find interesting.