The first thing I usually suspect in this situation is that the message aren't deleted but were possibly downloaded by an email client. Did you recently setup a new device to access your email or perhaps turn on an older device that you haven't used in a while?
Did you recently use an email client such as Outlook Express, Windows Live Mail, Outlook, etc. to access your email? I see a lot of POP3 activity on your account which by default deletes the contents of webmail when used.