If you are still on the old email format, check your deletion schedules to make sure they are set the way you want them. From the Inbox page, go to Preferences>>>>Email, and look about halfway down the list to "Email Deletion Schedules". If it's not that, then as a precaution I would change your password to something stronger than whatever it is right now, and also change your secret question and answer. Suddenly vanishing emails is a common sign of a malware infection or a compromised account. Run a complete scan of your machine with your A/V software to see if it finds anything wrong. There are no editable deletion schedules in the new format.
Also, do you have another device like a smartphone or tablet with the account enabled on it? If so it may be downloading and then deleting the messages from the server. Check all the settings in it to see if that's what's going on.