Try sending an attachment that is txt, from the other computer. When you receive the email, then check if it only had one attachment or had more.
It is also possible that the other user is in your blacklist. I haven't use OE6 in possibly 6 years, so I don't remember if it works with white/black listing, but if it does, try adding that user to the white list (allowed senders). This will also be valid for any anti-spam that you use.
Another thing worth checking is your message rules. From Tools>Message Rules (and here is also the blocked senders list).
Make sure you don't have any rule moving those emails to delete folder.
Finally, when the attachment is delete, is it replaced with another file, like a text describing why?