Is there another device or computer accessing the same inbox? If the other device is using POP instead of IMAP, emails will get deleted from the inbox on the server as they are retrieved by that other device.
Welcome to iMore.com! Sounds like you need to give us more info in order to help you. I think Michelfo is on the right track! In order to answer us you'll need to join the forum. It's REAL easy....