Magic Mouse draining Bluetooth keyboard batteries

There's a group of users on Apple's Discussion Boards who claim that their Bluetooth keyboards have been devouring batteries since they started using a Magic Mouse. Despite switching to rechargeable batteries and running all pertinent updates, the problem persists. Most of the thread's participants claim to need new keyboard batteries weekly.

Some have guessed that the Magic Mouse is preventing the keyboard from going into sleep mode. One user swapped his Magic Mouse with a Logitech model and saw the problem disappear, while another claims to have heard from Apple Tech Support that this is a known Bluetooth driver issue and that a fix is in the works.

This thread appeared on November 12, 2009, just a few days after Apple released Wireless Keyboard Update 2.0 on the 9th. The update was meant to "...use the function key one-touch controls of your Mac with your aluminum Apple Wireless Keyboard," and doesn't seem related to the battery issue.

The Magic Mouse was released on October 20, 2009, and is the first consumer mouse to have multi-touch capabilities. Together, the mouse and keyboard make a pleasant, clutter-free desktop, but aesthetics are worthless if you're constantly buying batteries. Have you experienced this issue? Let's hope it gets fixed soon.