I have one user on my domain running Outlook 2013 (Exchange 2010) with an additional mailbox to which he (and some others) have full access.
When viewing the mailbox with cached mode (Accounts > More Options > Advanced) enabled some emails are not visible; for no discernible reason. They are visible to other users with access to the box and are visible in OWA or when cached mode is disabled.
There is no pattern to which emails are not visible.
This has happened thrice now. A new profile fixes it for a while but it eventually reverts.
Office has been repaired, removed and reinstalled.