iPod won't play any purchased video

My iPod nano (4th gen) does not play any purchased video files anymore. Movies, music videos, you name it. Other videos (self-made) play fine. Some of the purchased videos DID play earlier, though I noticed the problem with a recent purchase (an HD movie, the first HD I tried to watch on the iPod. Naturally, it came with the SD version, which should be the one synced to the iPod). The movies play fine on the computer. When I try to start playing, the screen turns black for an instant, then returns to the movie list display. I already reset the iPod (with the reset option in iTunes), and re-synced all the video files.

What can be done?