With some administrator accounts, the user receives an email notification of a new conversation, but the conversation is not available within their inbox. This problem arose when upgrading to 1.3, and still exists in 1.3.2. This does not affect all administrator accounts.
This sounds like something specific to your setup as nothing changed in this area for a while. It could be add-on related. There are also tools in the control panel to remove all conversations started by a user.