I ran into this issue with my iPhone 4 running IOS 5.0.1. I plugged my iPhone into my Windows 7 PC to sync with iTunes and half way through the sync process a message popped up and said "This computer is no longer authorized for apps that are installed on the iPhone "Jason's iPhone". Would you like to authorize this computer for items purchased from the iTunes Store?" Then it says "If you do not authorize this computer, the app E*Trade Mobile" (and 3 other apps) and it's data will be deleted from this iPhone."
Then is gives me buttons for Authorize, Don't Authorize or Cancel. I didn't want to simply hit Authorize, because as you may know, you are only allowed to have 5 computers authorized for any particular iTunes account. And since this was the only PC that I use iTunes on, something was clearly wrong and I didn't want to waste one of my authorizations. I'd rather fix the actual problem. So I hit the Cancel button on the error.
You could first have a look at this article from Apple, but it didn't really help in my case. http://support.apple.com/kb/TS1389
My guess is that it is related to the fact that I ended up with two different iTunes accounts because I was a Mobile Me customer. I've had an iTunes account for a couple years and then I signed up for Mobile Me account (the predicesor to iCloud) and created a new account with an @me.com address. Then when Mobile Me merged into iCloud last year, the @me.com account also became an iTunes account. So now I've got two iTunes accounts and Apple doesn't provide any way to merge these into one.
So it turns out that I had downloaded a few apps onto my iPhone using the @me.com account without really thinking about the consequences. It looks like this decision is finally catching up to me.
So I went back to my iPhone and deleted the first app that the error mentioned - E*Trade Mobile. Then I started the sync process again in iTunes. The same error came up and mentioned a different app this time, because E*Trade Mobile was gone. I hit Cancel again and then deleted the app that it mentioned from my iPhone. I repeated this process 4 more times until I had deleted all of the apps on my phone that were mentioned in the error message. I'm assuming these were the few apps I had downloaded to the iPhone using the @me.com account instead of my normal iTunes account.
Then it was able to sync without any issues. And I had made a list of the apps that I deleted so I simply re-installed them using the proper iTunes account.
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