The process is a little bit of a hassle, but doable:
When you first get it into iTunes, use he iTunes menu and “Convert to AppleTV”
Once it’s converted, right-click on the AppleTV version to “Show in Finder”
Right-Click on it in Finder and open it in QuickTime.
Press Command-L to set it to loop, Command-S to save it
It should now be sync-able and playable on your AppleTV and it should loop.