Magic mouse loses connection with laptop unless laptop connected to charger

So, I've been seeing people have various problems with the Magic Mouse in Lion, but I haven't seen anyone with the exact problem as me. I lodged it as a bug with Apple, but I wondered if anyone has the same problem and maybe a solution.

I have an original MacBookAir and a Magic Mouse. Since upgrading to Lion, the Magic Mouse will only stay steadily connected to the laptop if I have the laptop plugged in and on the mains charger. If I am running the laptop on battery, the mouse disconnects and becomes unusable.