To resolve the issue of Outlook not properly updating or syncing calendar invitations or appointments, the following steps should be taken:

1. Verify that Outlook is set up with the appropriate calendar account.
2. Check to see if the calendar server is working properly.
3. Confirm the calendar has synced the latest updates.
4. Try to re-sync the calendar.
5. Check the junk email folder for any missing contacts.
6. Turn off the sync services and turn back on.
7. Restart the computer.