Does this user use OWA as their primary mail client? If so, I would then assume he is connecting via the Intranet internally to your network using company hardware and software configuration and over the Internet when out of the office, most likely at home?
If this is the case, gather some information regarding his home computer. Find out what OS he’s using, the type and version of his Internet browser and his method of connecting to the Internet (dial-up, broadband, etc.).
This may shed some light about his inability to connect from home. An older OS such as Win 95 or 98 with a browser version earlier than 5.0 (IE 5.0) or possibly another browser type such as Mozilla, Firefox or any other non Microsoft browser may be his problem.
If your using OWA 2003, suggest to your user the next time he tries to connect from home to select the ‘Basic Experience’ option for OWA (check box). Doing so will scale down OWA to to accomodate lesser hardware. He will not get all the bells and whistles as with the Premier Experience, but will be able to send and recieve email while out of the office.
Should his system be up to par for OWA 2003, have him try connecting this way anyway as it could provide some helpfull trouble shooting information.
Try to see if you can log on using his/her account from the Internet from a different computer. Like the above mentioned, try logging in using email@example.com or domainusername.
Do you host multiple domain names on your server?
Check IIS configuration, Exchange virtual directory, path to the directory, should be something like this (not sure if or how backslahes will show when posted).
Make sure that the user has an email address with your-domain-name.com.