They probably have a corrupt POP3UIDL.DBX file. Close outlook and delete that file. It will be recreated when you re-open outlook.
Please follow these steps on YOUR pc.
1) Click on “Start”
2) Highlight “Search”
3) Click on “For files or folders”
4) Search for “Pop3uidl.dbx”
5) Delete this file
This should correct the issue.
The .dbx file is a database file of downloaded emails. If this becomes corrupt it can cause duplicate emails or make old emails appear to be unread.