I had this problem this morning when I swapped the batteries over as the original ones the mouse came with were nearly gone.
The problem only arose when I changed the batteries over - not before. So it had to be something to do with the batteries. They were brand new, not rechargeables. I was very careful when removing and replacing the battery cover, so I know that was not damaged.
Suddenly I had the bright idea to measure the new batteries against the old ones. They were significantly shorter in length, despite being the same AA size. I happened to have some rechargeables in the same brand as the original batteries, and measured them. They were the same.
So my conclusion is that it depends on what brand of batteries you get/what they actually measure.
I haven't tested this properly yet as I'm waiting for the rechargeables to charge up fully - but if I'm right, it may help you to buy batteries the same brand as the ones your mouse originally came with.
HTH