Second
I also have started to notice this on my almost year-old ATV2. I've re-checked many times to make sure that it's anything but the Apple TV unit, but it looks like it is.
However, I've also noticed why it may have trouble recognizing your Apple TV as an authorized device. When i go to Settings>General>Sign in and attempt to sign in using my Apple ID and password, i get an error stating that the "Network time cannot be set." For some unknown reason, the Apple TV is connected to the internet, but cannot set the time zone and, i believe most likely for DRM reasons, will not allow the user to fully sign in. Note that everything else, for me anyway, is working as it should: Netflix works, non-iTunes purchased content, such as movies and TV shows, play perfectly, and photos stream through perfectly. It is ONLY iTunes-purchased content with DRM that will not play. Oddly, I can AirPlay this content to the ATV2 from my MacBook without errors or authorization obstacles, which is exactly as you describe.
I've been looking through other forums, discussions, etc. but haven't found an answer from Apple people other than the standard "reset everything" responses. I hope this is fixed once the next ATV update is rolled out, whenever that may be.