Make sure your iPod touch is updated to the latest firmware.
Apple support doc:
Once the movie is downloaded, you can watch it on your computer or transfer the rental to a supported iPod, iPhone, or Apple TV:
1. Connect the device and select it in iTunes.
2. Click the Movies tab (for iPod), or the Videos tab (iPhone or Apple TV)
3. Select the movie, and then click Move.
4. After all movies have been moved, click Apply in the lower right corner of iTunes.
You must be connected to the Internet to transfer a rented movie.
Additional Information
* After you transfer a rental, it is removed from your iTunes library.
* You can move the movie between devices as many times as you wish during the rental period, but the movie can only be played on one device at a time.
* Pairing needs to be configured to transfer a rental to Apple TV