Hi. Apple don't allow Adobe Flash player on their iPads. There are 2 protocols for viewing You Tube videos, Adobe Flash Player and one other. If the video is one of those (still a majority I believe) that requires Flash Player to view then you are out of luck on the iPad.
Further to the above. This link about the problem is one of many generated by Apple's policy... http://www.youtube.com/watch?v=MgUQ4xBIzrY
Ironically you can usually get you tube content on an iPhone because it's the provider that downloads it and re-transmits using a different protocol
The simplistic answer is that Flash Player stuck it to Apple's Quick Time and so now Apple is sticking it to Flash Player. Of course it's more involved than that. It's all about the protocol that will carry us into the future. The alternative is HTML (I think it's HTML5). YouTube is changing to HTML and phasing out Flash but it's a "work in progress" and now your download could be either. That's why you get some and don't get others.