Organizing and accessing contact information in Outlook.com
I believe that you are referring to a different issue than the one reported by the original poster. The root post refers to the "New Contact" button missing from Outlook online (OWA). The missing New Contact button would have no effect on existing contacts. That would be a different issue. Troubling, but different.
The reason that I make this clarification is to keep this post on track because I too am experiencing the missing New Contact button issue with Outlook.com via any web browser, but all existing contacts are still in place.