Thanks to everyone that has replied to this post. I have been experiencing simliar problems. I have a new Composite AV cable from Apple MC748ZM/A. (NOTE: This cable does not support video mirroring between device and TV) I've been testing only using youtube.
It appears that the cable does not seat as well on the iPad running iOS 5.1. I've noticed there is a little play in the connector. After reseating ("jiggling") the cable connector, the "TV out" option under General Settings appears and the youtube video also shows up on my TV.
The cable seems to seat better on my iPhone (1st Gen...yes I know it's dated...running iOS 3.1.3) where I don't notice the "play" in the connection and the video does not drop out even when I jiggle the cable connector.
The cable seems to seat well on a iPod Touch running iOS 5.1 but I am able to cause the video to drop out by applying pressure on the connector slightly which also ends the youtube video.
I initially thought it was an iOS 5.1 issue but I am now wondering if the connectors on the newer devices are slightly different than the cable connector. Maybe the iOS 5.1 is also slightly more sensitive to detecting the cable.
I am not sure how well this cable will work in my car so I am going back to the apple store and am going to test my cable and devices there.