I have been so frustated with the intermittent disconnects that I did my own investigation. The best clue was that different battery brands reacted differently.
I think people are chasing mostly red herrings. Nothing to do with bluetooth or other RF signals or software.
The answer lies in the battery compartment design, specifically in the depth of the hole for the positive battery terminal. In trying to be clever (to prevent wrong polarity insertion?) apple screwed up and made the hole fractionally too deep, i.e. the mouse positive contact is too far down the hole for some batteries.
Some of you are correct, that AA batteries are not all the same size. the critical dimension is the height of the positive terminal above the inner battery shoulder at the +ve end. ( inner because most batteries have slightly conical shoulders).
The longest protrusion of the positive terminal from the shoulder is found on the Energizer lithium and the Ikea, which have non conical shoulders and usually make contact if you don't bang the mouse around too much.
The shortest protrusion of the positive terminal from the shoulder that I have found is on the Duracell Ultra Power, which also has the most conical shoulder..
If Apple had reduced the depth of the well for the +ve terminal by just 1mm, all batteries would fit and work.
FYI, a few measurements of the +VE terminal length above the inner shoulder flange:
Energizer Lithium: 1.6 mm
Ikea: 1.6 mm
Ace: 1.4 mm
Duracell Ultra Power: 1.2 mm