That's good - so at least we know they arrive and don't get filtered externally.
As it is just one user - have you considered an Exchange database check?
eseutil /g - integrity check
eseutil /p - repair
eseutil /d - defragment
isinteg -s server -fix -test alltests
Please run the commands in the above order from a command prompt.
For reference: http://www.msexchange.org/tutorials/Exchange-ISINTEG-ESEUTIL.html
Alternatively, please export the problem mailbox contents to .PST file, delete the mailbox and then setup another mailbox, then import the mail back and see if that cures the problem.