I have 13 Office 365 Small Business Premium 2013 accounts and many of my users frequently complain that they cannot connect for long periods of time. I have had the same issue and it makes no difference which network I am on. I can access my sky drive while it is not working and none of the other applications seem to have any issue with connectivity.
If this was a permanent failure I would be looking at the settings, but it is not. I have checked for service interruptions and they are not as frequent as the failures. We do not have failure with all users all the time.
There are no issues if we use the OWA.
Please help!