I have thought for a while that I seemed to be losing some emails with 2013, but finally have some proof. I was looking at an email this morning sent to me last night, closed the email, went on to something else, tried to go back to it and it wasn't there. I have searched the whole database, and looked in deleted items. Finally tried "recover deleted items", and it wasn't there either. At this point I thought maybe I was going slightly mad and had imagined the email, so I used message tracking on the Exchange server to see that it it had existed, and had been sent to me. I can't think of a way to make this happen if I wanted to, I can only assume that since it isn't in the exchange recovery list, it is actually there somewhere but hidden. I will have to revert to Office 2010, if I can't trust emails.
For the sake of completeness, it is not visible with OWA or an Outlook 2010 client. I am accessing an Exchange 2007 server.