For the last week or two i have problems with resuming a tv seriers for example.
If i choose "resume 6 min" if it is where i left off, the loading wheel will just roll over and over again and not start the episode.
But i can start it for the beginning and jump to where i was, that works :p
Resume function works fine from my mac using chrome.
So it looks like there could be a bug in the AppleTV app