Apple Magic mouse problem
The issues you're describing very common, along with many reasons why; fortunately there are some workarounds that might help.

The first reason you could be losing connectivity is because many macs have improper antenna configurations for the Airport and Bluetooth modules. This causes the signal to either be extremely weak, or just flaky in general. It get's progressively worse if the batteries on your mouse are starting to run low - much worse! Another reason is the Mouse itself having an aluminum battery cover that shields the bluetooth inside of it from having a decent connection.

[Here are a few ways that might help resolve some of the issues] 

For starters take off the bottom battery cover and see if you have better responsiveness and connectivity. It works for me, although I have one of the macs with a backward antenna configs, so without doing that I basically have no connectivity. Another surprising fix is to download BTT (Better Touch Tool). I was very skepitcal about a third-party app helping remedy the situation, although I must admit that it helped tremendously. I'm not sure what mechanism the developer used to revive my mouse, but he's helped countless thousands I'm sure. If those two work-arounds don't do anything the last thing you can try is to re-wire your bluetooth antennna to hopefully make things work again.

The Magic Mouse has been plagued with these issues from day one, and besides getting another mouse that does the same exact thing there's not much else you can do. Oddly enough, the replacement that I got actually squeeks like mouse, and is worse than it's predecessor, which I'm currently wondering how to troubleshoot. Take a look at the article I've linked below; they might have a few other fixes that I might not have covered. 

Link: The Not So Magic Mouse