i realize that this post is a few years old, but i'm hoping the original poster might get notified. i am having this exact same issue, and it's maddening. i'm wondering if you ever found a fix.
my 3rd gen apple tv is directly connected to the router via ethernet, i can say that is definitively not a network issue, and the content streams beautifully. it's only when i pause netflix, i get kicked completely out and it takes me back to the apple tv menu screen. i have to log back in to netflix, chose which viewer, got to "recently watched" select the episode and then i can resume from where i left off.
also, am an IT professional (ACMT).
here's hoping @carboncow reads this, and here's hoping you found a fix or at least a cause.