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Hi David, my name is ***** ***** welcome to JustAnswer!
If you purchased the Surface Pro around Christmas, then you may simply be able to file a warranty claim for the stylus. For this issue, you'll want to go to the website for the Surface Online Service Center, which you can find at the following link:
On this page you'll see an option to check the warranty status of your service and find information on filing a claim. Alternatively, if you simply want to purchase another stylus you can do so from this site as well.
If you want to contact Microsoft directly via phone, you can do so by calling the customer service line at 1-***-***-****.
If you have any other questions on this, just let me know and I'll be happy to help you any way that I can. And before you run, please remember to use the rating box to rate the answer at least 3 Stars/OK Service so that I receive credit for assisting you.