Log into the Management Portal and review your logs to see if anything has come from this domain recently.
Do you have a subject line or something else that can help track down this message?
We have seen this type of problem when two domains used to share a mail server and one migrated off. If the domain configuration and mailboxes were never deleted from the old mail server then any e-mail sent to the old mail server would be placed directly into the old mailboxes and never forwarded on to the new mail server.
We have also seen problems when a domain moves DNS servers and the records are never removed from the old DNS servers. It can cause similar problems to the one mentioned above but usually results in a bounce message.