This is caused by multiple physical issues with the AA batteries and the MM battery compartment design. Biggest issue is at the ➕ tip end where the mouse battery case plastic is too thick and the contact holes are too small - so that 1) the plastic wrap around the battery hits the plastic and pushes the battery away from the metal contact. On several types of battery the plastic wrap is doubled over and provides more interference -- I scratch this material away - but it's not perfect. The tip is trying to extend to the contact, while the nonconducting plastic sheild is trying to provide lateral support for the front end of the battery. This is a big problem if something interferes mechanically.
2) Worse because many batteries have short tips with sloping sides, they have to be perfectly in the center of the hole to make contact. The sides of ➕ tips are sloped and they hit the side of the contact holes in the plastic sheilds (which are too small) - causing the battery to push away from contact when the battery is deflected sideways -- as in a jarring incident (where you hit the mouse on the table).
I put shim paper under the door to push the batteries to the center but the door bent, and the shims were not totally effective. In addition every time I changed the batteries I had to do it again -- the door should not be providing mechanical support for a component needing critical alignment (the battery).
Different batteries have different tip lengths, meaning that some are more prone to interference than others. I've tried several (Kirkland, Duracell, Eveready) but can't remember which were best. Note that Kirkland AAA batteries have a much longer tip than their AA batteries - so the battery manufacturers have slop in their standards as well.
The ➕ contacts in the mouse are also difficult to clean, since they are recessed.
If the ➕ contacts were metal cups instead of plastic sheild, then the tips would never be bumped out of the cup, and would not loose contact. My recommendation is that Apple create metal cups at the ➕ tip end to 'hold' the top of the batteries more securely, and maybe drop the plastic sheild or at least enlarge the hole or just put a contact bump/dimple facing each tip. Also, as an electrical engineer, I recommend whopping big capacitors to ride out voltage dropouts - or at least a safe low voltage halt state that would recover.
Still, it's my favorite mouse by a long shot.