This is a problem for many when using POP3 to download email. You could try using IMAP which is a syncronises your emails rather than just downloading without checking if its already done so like POP3 does.
If you can access your email via a website then logon and try and delete all the messages (Print and Save the ones you want to keep). Failing that contact you email provider.
Also try increasing the frequency OE checks for new email. Checking every minute can cause this problem.
Make sure you have not got the setting leave a copy of the message on the server. Again I have seen this setting cause the problem you describe.