I had this problem too, turns out a slight design flaw with the mouse is that smaller batteries come loose and power is lost, so the bluetooth dies. You'll probably find that it loses connection when you're moving it around quite a lot, in particular, when you lift it up off of the desk and put it back down again. See, different brands of battery tend to be ever so slightly varied in size, and smaller ones tend to be more 'loose' in the mouse and an be shaken loose when moving the mouse around.
The best solution (the one which worked for me) is to grab a set of Apple's own rechargeable batteries from their store as they are just the right size to fit in the mouse without ever being shaken loose.
If you can't do this, some people find that wedging a bunch of paper between the two batteries and between the batteries and the mouse door can help keep them in place.
I hope this solves your problem as it has mine. 🙂