I was thinking that the purchase might be hidden.
iTunes Store: Hiding and unhiding purchases
Or perhaps the Apple TV is not signed in with the Apple ID that was used to purchase it.
Sign in to the iTunes Store
- From the main Apple TV menu, choose Settings > iTunes Store.
From: How to rent a movie from the iTunes Store on Apple TV
If you check in the settings and you are signed into the iTunes Store on the Apple TV with the correct Apple ID, and you have also verified that the purchase is not hidden, then I would recommend contacting the iTunes Store support directly with this article: How to report an issue with your iTunes Store, App Store, Mac App Store, or iBookstore purchase found here http://support.apple.com/kb/ht1933.