I was having that same problem. The only fix I found was someone telling people to just go to Youtube manually through the web which is fine, but would be nice to have the app.
It works with the 132 update, but there is a glitch that can only be remedied by exiting the program and starting it up again. The keyboard pops up, but when you want to hide the keyboard, you can't because the BB menu appears BEHIND the keyboard so you cannot HIDE the keyboard. YouTube needs to fix this.
Strange thing I noticed. My storm is 3 months old and came with you tube app. Just bought my other half a storm and it shipped from Verizon with no you tune app. I think they realized the bandwidth this app encouraged folks to use. Why else would they stop shipping storms with the app?