Also experiencing this issue. Went to the beta builds and installed the last 10.8.1 build, and connections are restored.
I wonder if this has to do with point 1 of their whats new (release notes for the latest build in the Mac App Store):
On the new feature front, we:
• Integrated support for the new RDS AAD Auth Protocol which is used for authentication and session security.
• Added deterministic progress UI for AVD workspace refresh.
More in the sense that making changes to auth as a whole broke other types of auth.
ImagineThisBen no official way to get back to the non beta (since they are only hosted in App Store), but im almost certain that in the beta builds list, if you go to the final 10.8.1 build, that build even though listed as beta in the list, is actually the release build submitted to the App Store. The last 10.8.2 beta build is the app store release build