Normally, this is a symptom of a corrupt or stuck email at the server end, but can also indicate corrupt account settings at the client. What happens is that the POP3 client issues the receive command 1st and when complete issues the delete. If server or client disconnects early, the delete never happens, and you download the same emails over & over again.
Deleting the email account and re-adding will only resolve if the issue was on the client end. If that doesn't fix it, check the web-based interface against your downloaded emails, and remove the first one you haven't downloaded from the queue - this normally means read and delete.
If this happens a lot, ask your host if they filter out email that doesn't comply to the appropriate RFCs.