I, too, am using a Microsoft Arc Touch Mouse Surface Edition. I really like the mouse and haven't had any connection issues with it, but have had ongoing issues with the touchstrip used for scrolling. I find that it works quite well, but it will randomly conk out and quit scrolling on me. A simple reboot of the mouse (yeah, I know. Now you even have to reboot your mice to make things work!) by flattening it out to turn it off and then curving it again to turn it back on always restores the functionality.
From what I've read on the Internet, this is a fairly common problem with this mouse. If cdf3, above, hasn't experienced this with his/her mouse, perhaps I'll see if MS will replace mine and I'll try another one, as I've now experienced this problem on both my SP2 and SP3, which does kind of point to the mouse having an intermittent hardware issue.
When looking for a Bluetooth mouse, it always amazes me how few options that there are available. Most every notebook built in the last several years has Bluetooth built in, so I would think the market for Bluetooth mice would be considerable, but apparently it is not. My experience with Bluetooth is that it is much more reliable for mice and keyboards than those that use the proprietary USB wireless adapters.
Finally, I also use an Apple Magic Mouse with my regular work laptop and have never experienced a problem with it. Maybe it's time to get one more for the SP3.