I always have trouble with YouTube on my iPad. Now every time I sign in it says "YouTube unavailable", it's been doing it since last night. I cant watch any videos either...somewhat annoying. Internet works fine as I'm typing this up on my iPad.
I can confirm the same issue. I have five users currently reporting this, with emit makes 6. A quick search shows this problem appears to have started yesterday.
My login for youtube broke last night too I guess. I found how I got the youtube app that does let me login to my account and stay logged in.
Go http://m.youtube.com/ in Safari and then login to your account. Then you can hit the + button and click the "Add to Home Screen"
I've ALWAYS had a problem with the YouTube app. Is works fine but it's just my subscriptions. First 4 in the list work and any after that just pops up the the "YouTube is unavailable" crap. I don't bother using the app anymore as I find the mobile site to be much better!