An error in the registry at the following location can prevent Microsoft Outlook from remembering passwords for E-Mail accounts:
HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\User Shell Folders
It can be fixed by resetting the entries back to the defaults. The easiest way to do this is the download the file below (usershellfolders.reg) and double click on it. Click on Yes to allow the changes to be imported, then try setting the password in Outlook again.