Magic Mouse keeps disconnecting from bluetooth

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.

In the console logs, I get these messages:

10/31/09 6:06:20 PM kernel [0eb48f00][AppleMultitouchDevice::willTerminate] entered
10/31/09 6:06:20 PM kernel [0eb48f00][AppleMultitouchDevice::stop] entered
10/31/09 6:06:24 PM kernel [0ffa3600][BNBMouseDevice::init][30] init is complete
10/31/09 6:06:24 PM kernel [0ffa3600][BNBMouseDevice::handleStart][30] Done
10/31/09 6:06:24 PM kernel [08701100][AppleMultitouchHIDEventDriver::start] entered
10/31/09 6:06:24 PM kernel [09f11680][AppleMultitouchDevice::start] entered

The first message is when the mouse disconnects, and the rest are when it reconnects.

Does anyone have any suggestions?