I've recently found a workaround for this. In iTunes (which is where I assume the video is) select the movie, and then go to Advanced -> make iPad version.
It will create an .m4v formatted video that will play on the iPads without issue. But now, for the looping, copy the video to iPhoto, in an album all by itself. Sync the album to the iPad.
Make sure on the iPad your settings for photos has Loop slideshow turned on. THen go to the photos, open the new album and select Slideshow.
It's an unnecessary workaround, but it does work flawlessly.