What to do when your iPad keeps asking for the iTunes Store Password

Question

I was using my iPad last night when it just started asking for my iTunes store password and I was browsing the web in safari. I just entered it and scratched my head. Later I was playing a game - the same prompt interrupted the game.
http://skitch.com/mbrad/dru2p/full-screen
It happened about five times before I finally went to the settings app and signed out of the app store. I don't think it's related to any one app since the prompt was happening at seemingly random intervals no matter what I was doing (even on the home screen with no app "running")
Signing out seems to have corrected the problem. Apps still run and I will try signing in again later once I need to download anything. I haven't done much other than update 5 apps earlier in the day.
Does anyone else have experience on what caused this?
Here's what it's not:
1) Time - I checked the date/time on the iPad - they were within seconds of my mac which sets time automatically on the internet.
2) Password wrong - I downloaded a free app from the store app on the device after entering the password - so the password was fine for a purchase/download after the prompt. (Yet the prompt came back again within 30 minutes)
Thanks,
Mike

Answer 1

Thanks for the suggestion! I did have two downloads for free songs I got from a card at Starbucks. They started but never came on my iPad (and that was 4 days ago). The store error is happening only yesterday - possible but a long time after the "failed download". I just got those songs after your suggestion on my mac by checking for available downloads. Maybe that was the root cause?
Add rebooting to "here's what it's not" - I forgot to write that down. Also - I was not interested in restoring the iPad - like taking a firehose to water a flower, that certainly would fix it at cost of overkill. (and maybe only until the backup was restored if the file causing the issue is something that would be backed up).
The problem seems to be that the device either doesn't save the password or something is causing it to be periodically marked as bad. Both ideas have me scratching my head. Rebooting didn't resolve the issue - only signing out from the store.