There may be an issue with the data connection or the iPhone or iPod touch might have downloaded an invalid URL for the YouTube video when it initially played on the device. Since the invalid URL is now cached on the device, playback for that video might not work when you attempt to replay the content. Restoring the device or manually deleting and then re-adding the video to the unit should resolve the issue.
Verify if the issue only occurs with one type of data connection when trying to play or view your YouTube video/movie. For example, if using an iPhone 3G, does the issue occur only on EDGE, 3G, Wi-Fi or all of the above? YouTube will normally not play movies or videos on iPhone if only a GPRS () data connection is available.
If you cannot view or play the YouTube video on the iPhone over EDGE and/or 3G but it works fine on Wi-Fi, the issue could be due to a data connection from your carrier. Please contact your carrier for assistance.
If the YouTube videos you cannot play on iPhone or iPod touch were bookmarked on the device, manually delete your video bookmark(s) and then re-add them to your device by using the Search feature to find the video. If the YouTube video that you want to view is in the "Most Recent", "Top Rated", or "History" category, clear the list and re-add them to the device by using the Search feature to find the video.
If you cannot view or play YouTube videos on iPhone or iPod touch over any data connection, restore the device in iTunes. After restoring your data from a backup, see if the issue is resolved.
If you're not able to view YouTube videos over Wi-Fi, contact your Internet service provider.
Note: The features and troubleshooting steps above may not be applicable to devices sold in certain countries including China. Please see iPhone or iPod touch technical specifications and this article for more information.