Microsoft ends its support for Windows XP inc Outlook 2003, find out more.
You can solve most problems by installing the latest updates, the most important of which is Service Pack 3 (the current version for Outlook 2003).
Not sure which Service Pack you have?
Installing Service Pack 3
You can get help installing Service Pack 3 from the Microsoft Support website.
For a better experience, you may want to think about upgrading your MS Outlook 2003 version to MS Outlook 2007/2010.
After you've installed Service Pack 3
When you've updated to Service Pack 3 you'll need to check that your default settings for sending email with Office 365 are correct. They should be:-
SMTP default settings
If you've installed all of the updates and you're still experiencing problems, try changing your settings to those below. If it still doesn't work, you'll need to upgrade to a supported client like Outlook 2007:-
SMTP alternative settings