I have a similar problem. I've swapped out the mouse for two others. Same result. I swapped out different batteries. Same result. I've swapped out a different charger with different batteries. Same result.
I don't think it's a problem with the batteries, mouse, or charger. It's the Mac, and maybe more specifically, Bluetooth. But I don't have a solution.
I agree with Ron. I'm the tech support for our group, and we have one newer macbook pro, same as two others in office, it has had persistent intermittent Bluetooth issues. I've swapped my Magic Mouse for that one, and the problem stays with the Macbook, not the mouse. On my MBP I never have disconnects and the batteries seem to last longer than most report. On the other MBP, I can reset the PRAM and it's good for awhile, but eventually it starts having issues again and the MM eats the batteries all the time.