I'm not too sure what I did to fix the same problem with the authorization loop, but it something I did worked. I was frantically searching around for info on this and just did the following:
**BTW, I am on Mac OSX 10.6.8, issue was authorization loop while trying to update apps on iPad2 version 4.3.3
1. I went into Safari and chose to "reset Safari" menu -> Safari -> reset Safari. I selected all and reseted. Then exited the app completely.
2. I logged my out of my appleID on the iPad and shut it down.
3. I also cleared all cache, history, cookies, etc. in Firefox, and exited the app.
4. Opened Itunes, logged out, and exited app
5. opened Firefox, and changed my account info at:
http://store.apple.com/1-800-MY-APPLE/WebObjects/AppleStore.woa/wa/RSLID?nnmm=ac ct&sf=wHF2F2PHCCCX72KDY
6. I first changed my password, then...
7. I switched C.C. info
8. Changed my address from "123 S. Abc St." to "123 Abc St." ommited "S."
9. updated it, then logged out, cleared history, cache, cookies, etc. and exited Firefox.
10. Opened Itunes, logged in (with new password), logged out, exited.
11. Turned on iPad, logged in (with new password), removed "Payment Information" in Store settings (in Settings)...
12. Closed Settings, opened App Store, and updated. it worked!
Not sure if this will help anyone, but something I did worked for me.
Good luck in your solutions...