We'll need a bit more info, check your logs and see what they say. Check first (assuming slackware):
/var/log/messages
And then check /var/log/mail and so on. You should get decent info on what's not working out. And there should be a rejection code, or more to the error message than just "failed" so if you can post that up as well, that'd be great
Here's my SWAG though:
make sure that the directory that your mail is being delivered to exists. If you are using courier-imap and Postfix, I'm assuming you are using Maildir's. If your users don't have the .maildir or Maildir that is needed (check /etc/courier-imap/imapd for what directory it's gonna look for) then it will fail.
Good Luck!
Cool
