Once I turned off the "antivirus" option for the user, no more blank e-mails come in.
Here is the header of one.
X-Spam-Checker-Version: SpamAssassin 3.1.0 (2005-09-13) on keynes.mpsge.net
X-Spam-Status: No, score=3.2 required=5.0 tests=EMPTY_MESSAGE,MISSING_HEADERS,
I have experienced this with another account on another domain and turning off the antivirus seemed to fix it as well. I would really like to scan the messages as they come in so leaving this turned off does not agree with me too well.