I have a user that recently changed their password for Office 365/Exchange Online. After doing so it won't let her sync her Outlook 2010 and keeps asking for a password. The password she is using is correct and we tested it by going through the Outlook portal online. Also, I was able to setup Outlook 2010 on a different computer using her credentials without issue. Further, I was able to setup Outlook on her computer using my credentials. So the problem doesn't appear to be Office 365 based as she can sign in online and she can sync with Outlook on a different computer. But the fact that I can setup Outlook 2010 on her computer using a different problem tells me it's not a computer issue either - unless there is something stuck somewhere on her computer that won't let her use the new password.
I have tried clearing out the whole mail profile (Start - Control Panel - Mail (32 bit) and try recreating the profile several times with no luck. Each time it finds her profile but then prompts her to put in the password she just put in. It won't get passed that "Windows Security" box that pops up looking for the new password.
I also tried clearing out any files within the c:\users\-username-\appdata\local\microsoft\Outlook folder but the problem remains.