Yes! I am having this exact same problem and it is pissing me off... It was all working fine and dandy (I was able to download stuff on my iPhone) and then all of a sudden I couldn't log on to iCloud online.... and now that I upgraded to iOS 6 and told it to do iCloud backups it wants my password and says its not valid (but I can still download apps). I really don't want to change my password again because well I quite like mine lol
I've had this problem several times and was stumped and annoyed that I had to keep changing my password and fixing it in all the places I'm logged in with my Apple ID.
I have the answer! I called Apple tech support and they know why this is happening!!!
At some point in the past, when you went to appleid.apple.com and logged in, under the "Password and Security" option, there was a setting that allowed you to manage how often your password would expire, ie. every 1, 3, 6, 12 months... you get the idea. Well, in the recent past Apple made some changes and security enhancements to better protect peoples' private information, and guess what? They have since removed this option. One of the Senior Technical Advisors who knew exactly what I was talking about (and had intentionally turned this setting on for themselves) went into their own account, but alas, it the option was not there.
Unfortunately, at this time, however often your password was set to keep expiring, it will continue to do so.
A possible solution in the future?
Call AppleCare 1-800-275-2273 and ask them (try to speak to a Senior Advisor) to put in a formal request to the "powers that be" to either permanently stop all accounts from having their passwords expire, or make a request that Apple return the user's option to change their password expiration setting. Or both. The more people need something to change, the more likely Apple will be able to make it a priority.