I had a user who had a similar problem with his home email account. In his case it was due to the anti-spam software running on the ISP's mail server...sorry I can't remember more details.
I poked around a little onlne and found these links:
http://kb.iu.edu/data/ahph.html
http://www.askdavetaylor.com/outlook_2003_on_windows_xp_retrieves_duplicate_emails.html
The first link suggests network connectivity problems combined with the "leave message on the server" setting, among other possibilities. The second link points to anti-spam software running on the server causing problems...it suggests that AVG or something similar tags the message after scanning which results in a loop where the server sees every tagged email as a new message.
Another thing to try is to increase the time intreval on the client's send/receive. The logic behind this is that a bad / slow connection to the mail server combined with a frequent send/receive interval "confuses" the server.
Do you know what software is running on the mail server (OS, mail server program, antivirus / antispam)? Are the problems only on this one client's PC? Does the problem go away if you set up a different email client on this PC? WHat if you set up the account on another PC?
I'm inclined to believe the problem lies with on the server end, but rule out other causes by setting up the mail account on another PC and with another email client. Send test messages and see what happens.
To paraphrase Sherlock Holmes, eliminate all of the wrong and what's left is right. I'm not very eloquent today, but I think you know what I'm saying.