Apparently, there is a small selection of users that have found that the stylus stops working after a while. Normally, when it's a small set of users, it can be chalked up to an odd bug, but this one seems serious enough that Microsoft is looking into it. There have only been a few reports in the Microsoft Answers forums, but no one has found a cause or fix for the issue. It seems that some users are finding that the stylus will work fine for a time, then simply stop. And, even uninstalling and reinstalling the drivers only offers a temporary fix.
Microsoft has admitted that there are some issues with the stylus that are planned to be addressed in a coming update, and has also confirmed that it is looking into the new issue. That's some solid support from Microsoft. It's always nice to see companies proactively addressing potential problems rather than ignoring them until they hit a certain media threshold.