É um problema conhecido: Vida útil da bateria no mouse mágico puxa um ato de desaparecimento
Aqui estão duas dicas do link acima.
The Magic Mouse is supposed to go into hibernation when it detects a lack of use, which should help extend battery life. Turning the Magic Mouse off manually when you're done using it, with the switch on the mouse's belly, should help push battery life a little further.
Another option to get the most life out of the Magic Mouse's batteries is to replace them with either Lithium-Ion AA or rechargeable NiMH (Nickel Metal Hydride) batteries.