I found this the hard way myself and finally realized how the cover is locked. Apple should put this on their documentations for the Magic Mouse.
Do these steps:
- Turn the mouse upside down
- Locate the black stub at the bottom that hinges the cover to the mouse.
- Insert the cover at the top edge first and then press it in at the bottom
- Push that black stub in the direction towards the top of the mouse.
This step  should lock the cover. I found it by chance that the black stub can move down and up. It is spring driven. If the spring loses its strength, it may not pop UPwards that easily when you press the cover into it. All you need to do is to push it up and it will lock.
I have tyhe SAME problem... BACK COVER... LOST !!! and I took SPECIAL CARE not to loose the derned thing... obviously didn't work and APPLE dopesn't care either.... They DON'T REPLACE the back covers... or at least not mine ! Friggin CHEAP Steve Jobs & his people !! I don't get it !!
All the answers are rubbish.
It was inherently designed not to grip the latch firmly. If I move the mouse widly, the cover falls off.
It's a design fault.
The problem worsens if I use a pair of rechargeable batteries. (i.e. Energizer)