Comment by jonpurdy
I had an issue with the original Apple Magic Mouse that would not work correctly with NiMH batteries but work fine with disposable AA. The mouse would be fine for a few days then randomly stop working; using fresh NiMH would revive it again. I assumed it was due to 1.2v vs 1.5v but perhaps that particular mouse (or all Magic Mice) was just bad.
Apple sold their own NiMHs (actually rebadged Eneloops) along with their own AA charger to go along with the Magic Keyboard/Mouse, so my bet would be on a faulty device. https://en.wikipedia.org/wiki/Apple_Battery_Charger