This is not my fix but glad to pass along something that actually works. Give Kudos to the "how-to-Geek" and post in other forums to help out all your frustrated friends.
1. Close outlook!
2. Go to my computer and then paste this into the address bar. %userprofile%\AppData\Roaming\Microsoft\Protect.
3. Rename the very long file name S-1-5......etc by appending "-old" to the end of the existing file.
4. Now re-open outlook and you may be request for your password. If so enter it and check the remember password box.
5. Now go back to %userprofile%\AppData\Roaming\Microsoft\Protect by searching in windows explorer or my computer and you should see the renamed long named file and a brand new long named file.
This should work for you. If not, then do a shut down and reboot a time or two. Then try reopening outlook 2010 and your problem should be fixed. Save this link: http://www.howtogeek.com/howto/windows-vista/fix-for-outlook-2007-constantly-asking-for-password-on-vista/ because this problem is likely to recur sporadically because of microsofts pushed updates that cause more problems than they solve. Turn off automatic updates so MS cannot keep screwing up your system and snooping.
This fix was explicit for Vista but worked fine for me on Windows 7 64 bit running outlook 2010. Post your results to see if it works for others please. I know everyone is tired of chasing their tails on this problem and even posted fixes have been so vague that you need to be a software engineer to follow them. If you have other fixes for this I know everyone would appreciate people posting all the steps from the beginning to end and assume that we know nothing at all. Post all the paths and explanations in simple terms please.
I hope this helps.