Thanks, that fixed it.  The emails were not deleted, just hidden because of that setting.  I had just reinstalled Windows, etc.  Apparently, the older messages, even though they were restored from a backup of my mail folders, were not marked as read, and thus were not hidden.

I have been using selective download so that I can refer to messages via webmail when not at home.  Since a couple of days ago, the messages were deleted from the POP3 server, even though the setting does not appear to have changed.  Any solutions?

Make sure the POP3 server is NOT setup to offer up only unread mail.