Tested: OL2013 + Win8 + roaming user works on a Windows 8 machine on the same LAN - but not on Win 8.1. SMTP runs on port 587 with TLS and in Outlook 2013 returns 0x800ccc0f (interrupted) on Win 8.1.
The PC with 8.1 used to work before the upgrade from Win 8 to Win 8.1. I simply took the same user account (roaming) and logged into another PC with Win 8 and OL 2013 ... no problem before Win 8.1?
So switch Win 8 with Win 8.1 ... and interaction with stmp.live.com seems to stop working correctly.
Here is another post which may relate to this: http://social.msdn.microsoft.com/Forums/vstudio/en-US/5555297a-3b32-41f4-aedf-666825a9f0c0/cant-send-email-to-hotmail-on-windows-81-os#de455dfc-88d8-49e0-b039-8249c829abdc
BTW: No problem with POP3 (port 995).