A few people have noticed Apple's new multitouch "Magic Mouse" will disconnect at seemingly random times. When the computer is booted the mice connect just fine and are usable for a while; however, they will soon become unresponsive and the "Connection Lost" icon will float at the bottom of the screen.
When this happens, people have had mixed results with trying to get the mice reconnected. Some have claimed that just clicking the mice will get them to connect again, and others have mentioned tapping it on the case of their desktop computers was how they get it to connect.
This problem appears to be with the mice losing power when movements jar the batteries slightly. In some cases people have been able to cause the mouse to disconnect by holding it up from the trackpad and firmly tapping on the top side of the mouse. This suggests that slight battery movement may cause the mice to lose power, and as such there are a couple of remedies available:
Re-seat the batteries.
If a small misalignment is causing the batteries to easily disconnect, try taking them out and putting them back in. This will exercise the spring mechanisms that hold the batteries in place, and perhaps cause them to apply a better hold on the batteries.
Wedge paper under the batteries.
Some people have had success in rolling up a small wad of paper and placing it between the batteries before closing the cover. This will put some additional pressure on the batteries to help secure them in place. If you do this, be sure you do not put so much paper that you warp the battery door.
Replace the batteries.
If your batteries are running low, the mouse may start behaving erratically and disconnecting. However, if this is the case the computer should report the battery level as being at critical levels, as long as you have installed the Magic Mouse driver software.
Apple has a recently released knowledgebase article that covers a number of issues people are having with their bluetooth devices, including the Magic Mouse. Unfortunately, even though they mention random shut-offs, they only suggest checking battery levels and checking for interference as possible solution.