The same thing is happening to me, and I am especially concerned about it as I am going to be getting the new iPad on March 16. With my current ipad 2, I can download updates and sync with my iMac. But when I do try to sync, iTunes keeps asking for my password on my iMac. If I do nothing and ignore the request, it continues to sync anyway.
I am guessing that the problem is caused by having a different password for iTunes on my iMac and another one for updates and purchases on my iPad 2, although I wasn't aware that this even happened. I suppose I could reset the password on iTunes on my iMac, but this is a real pain. I read that it is possible to have multiple Apple accounts and Apple does not allow consolidating them, which is a huge pain. If this is the problem I am having, there is no way to consolidate my accounts. I am expecting major stress when I get my new iPad and try to set it up. Grrrrr....
The solution (for me at least) is to keep trying the same password that I know is correct. For me, the fourth try of typing in the exact same password works in iTunes on my iMac. I have repeated this several times, and each time it works.
I also reset my password, but the same problem occurs in iTunes. I have to type in my password four times in iTunes to get it to work.
iTunes is having issues. I can log in easily on the first attempt every time to post on this message board and I can sign in easily on my iPad 2 to get app updates, but in iTunes on my iMac it takes four attempts and then it works.
Apple needs to release a statement to the public telling people abut this. For Apple to know that this iTunes problem exists and that it is causing literally thousands of people to be stressed out is callous and uncaring.
iTunes incessantly asks for password when you "Reset Safari"! Yeah, I know... What The Frick?!
Not having tested each one, I'm not sure which of the reset items causes the problem. You can check it yourself by NOT resetting Safari and restarting your Mac, and launching iTunes - then RESET Safari and restart your Mac and launch iTunes.
Not a fix, but at least we now know why!