I'm using the Surface Edition of the Arc Mouse and it was having the same issues where it would stop the scrolling until I rebooted the mouse. I ended up looking at the settings for the mouse. I didn't even realize there was a Page Up/Down option (and have obviously never used it). I tried turning that off about 10 minutes ago and my scrolling is still working great!
Before I changed that setting, my scrolling would stop after 2-3 times of using it. I don't know if the same solution will work for previous revisions of the mouse, but it's worth a shot if you haven't tried it yet.
(I just successfully scrolled again! I never thought I'd be so excited about my mouse scroll actually working.)