Try these steps to find out what’s going on:
1) Have the sender e-mail you with you listed on the TO line. (have subject indicated TO test)
2) Have the sender e-mail you with you listed on the CC line. (have subject indicated CC test)
If you get step 1 with no issues and step 2 with no attachments, then I would lean towards being an Outlook rule where something indicated with you listed to on the CC line.
You may also want to check and make sure it is listed on the Sent Items of the sender.
Furthermore, some Content and Spam Filters will trash messages with certain keywords without any notifications whatsoever (for instance, the term “cocktail party” can be flagged for the wrong reasons).
You can also check the Exchange Manager for Sending/Receiving message limits, although Outlook should send a warning anytime you exceed the file size limit in an email.