I am having the same problem as described by the other users above. I bought the Arc Touch mouse yesterday, opened the mouse, inserted the batteries and the mouse worked ok for around 2 minutes. After 2 minutes, the scroll strip became unresponsive, it would work for perhaps a stroke and then stop working. The left button would also stop working.
I un-installed and reinstalled the software, just to be sure. Still the same problems. I then decided to try a fresh set of AAA batteries, after which, the Arc Touch worked perfectly! I have used the mouse for around 30minutes to an hour at most, and now the problems are back again. The batteries I inserted into the mouse were fresh. Surely this mouse doesn't drain a set of AAA batteries in this amount of time.
I agree with one of the above comments, perhaps there is a software of electronics problem with this mouse. I am going to try another set of fresh batteries to see if this addresses the problem. I will give the mouse one more chance, if it continues to behave like this, and there is no response here from a Microsoft Representative, then I will return the product and swap it for something that works consistently.
If it is a hardware problem, it is a shame, as this is one of the nicest products I think Microsoft has produced, and when it is working, it's brilliant.
Eagerly waiting an update from a MS Arc Touch Mouse rep...