I have had this issue a couple of times and it is a frustrating one.
With Exchange 2010 - 2016 you get some Outlook clients that will no show new mails until you close outlook and re-open it again. This issue continues even after:
- Rebuilding the profile
- Repairing Office
- Deleting the OST files
- Rebuilding the send/receive group
Now I cannot tell you exactly what the cause is, although it is connected with the authentication and, in particular, the setting that MS Outlook has whereby it is set to 'negotiate' the security principles. If you change this setting to NTLM or clear text or (maybe) even Kerberos then mail flow will begin again and you will see new messages in your inbox.
Just in case anyone gets stuck with this.....