Did they receive any mail in that period? If not, is he using Outlook in cached mode, and for some reason have been offline? Not all users notice that they are in offline mode, and does not understand why mail is not sent or received
Have you got message tracking enabled? If not then you are going to be a little limited on what you can do.
Are these internal or external messages? If external messages check the SMTP headers to see when the messages were delivered to the server.
You need to be very clear on what Message tracking shows as it makes a difference as to where the problem is/was.
If you think there are messages in message tracking that are not seen in Outlook, then check the account using OWA to see whether they can be seen there.
The most common reason for email disappearing and then reappearing is a view was incorrectly set.
Then I have also seen a user setup a rule to delete all email, then when the boss wants to know what happened to the email, the user recovers it from the deleted items folder and then blames the server.
Message tracking is your best tool here, because if it shows the message being delivered, then it is in the mailbox and everything that happens from that point on is a client side issue.