Addition: A few days later, the trouble returned. I discovered "Leave a copy of messages on server" was checked. Attempts to access the POP account via Mail2Web.com failed, but the hosting provider's own webmail worked just fine. Messages sent to the affected address were failing with a bounceback stating the user is over quota. After clearing "Leave messages on server" and attempting access via web and Outlook Express several times, the trouble cleared itself. At this point I noticed a rather large email was received a day ago.

I conclude that the mail server became confused about the available space of the user's mailbox quota. For some reason, it acted as though there was no space available even though the mailbox was empty. This seems to be the reason for the errors received while attempting to send mail.