This is the way POP3 client works :
1 - It connects to the server and gets the list of emails
2 - Start downloaing ALL of the emails.
3 - After finishes the last email, it tells the server to delete the emails from the server.
In your case, the last part (3) is not being done and in most cases the your pop3 client connection gets disconnected by the server in the middle of part (2).
That is why the next time it connects, it starts from the beginning.Most probably this happens because the connection between the server and the client gets interrupted. It could be an antivirus program which detects the virus and stop the connection. There is no solution to this because it is how POP3 protcol works, however you may want to delete the already downloaded emails trough webmail.
Updated Jan 26, 2005:
Make sure you are not using BOTH webmail and pop3 or using both IMAP and POP3 at the same time, Webmail and IMAP can both lock down the server, emails will be received, but they can not get deleted, so the next time your pop3 clients logins, it receives them all again and again .