Is this MobileMe account accessed by more than one computer or device. If another computer (or even just another email client) is accessing the account, make sure that it is not setup as POP. Where permitted, accessing an IMAP account as POP with another computer, and where that is set up with the POP option to remove from server after some time period, one of which is typically one month, is the leading cause of what you are reporting.
Ernie