This problem normally happens with Outlook users. Interruptions in the download process cause Outlook to hang on download. Then, the next time you do a send/receive, it starts downloading all the messages over again until it hits the interruption. Normally, the interruption is caused by a spam message stuck in your inbox due to a message that has incomplete mail headers.
To remedy this, log into your webmail account and delete all spam messages you see, especially those which have an empty "From" address. Then, try the Outlook download again and it should download completely.
If that does not remedy the problem, check to make sure your Internet connection is working correctly and not timing out during the download process. Interruptions in the download process cause Outlook to think the download never happened, so next time you try to download, it starts from the beginning again.
