If you get caught in this loop, "Would you like to Authorize?" "You already are" "Would you like to Authorize?" "You already are" "Would you like to Authorize?" "You already are"....
Try... Deauthorizing under the Store menu. Then Authorize again. I think that might fix it.
Unfortunately, I got caught in this loop and I tried a Restore and now I have an ipad with just a few default apps on it. Then I tried the above and it seems ok but it's going to have to re-sync thousands of songs and pictures first. Good Luck.
.....later that same day
Maybe I haven't fixed it after all. I got an alert that I had some unauthorized stuff on my computer. Winnie the Pooh (the free book) was one of them. Also a few songs I think I downloaded for free from the store (Free song of the day). If I try to authorize it doesn't work. So I just deleted those few. Other songs I paid the 99 cents for are ok I guess. Because I have purchased entire albums but really only 4 problems were on the warning list. Weird.
My best advice now is, don't touch anything.