If Outlook 2007 is constantly asking to enter your password, even though you've enabled Remember password, try the following:
Close Outlook.
Navigate to: %userprofile%\AppData\Roaming\Microsoft\Protect (Vista/7), or %userprofile%\Application Data\Microsoft\Protect (XP).
In that folder should be another folder named after a SID. Rename or delete the folder.
Some people have reported a reboot is required before starting Outlook again. To be on the safe side, do this. After the reboot, start Outlook again. It should be fixed.