What would cause some e-mail to be flagged to the sender as Not Accepted?
If the sender is sending you many e-mails at once, their ISP may think it is spam and reject it. Your mailbox may be full. If you have your e-mail program set to leave a copy of the message on the server or you have several very large files come in before you check and download your e-mail, you may have gone over you allotted mailbox space thus causing additional messages to be rejected.