I'm having the same issue a lot of people seem to be suffering trying to make CRM 2011 for Outlook 365 work. I get the "There is a problem communicating with the Microsoft Dynamics CRM server. The server might be unavailable....."
I have tried all of the solutions I can find on here including :
Uninstall / reinstall CRM for Outlook
Repair Outlook
Uninstall / reinstall Windows Live ID Assistant (v6.5)
I've worked my way through the on-line troubleshooting wizard and NOTHING works!
The configuration window that pops up in Outlook seems to show my login as correctly authenticated and it correctly identifies my organisation when I select "Test Connection" but when I then choose OK I get the error I stated above.
What's most annoying is that this worked perfectly until about three weeks ago. Office 365 status reports were then showing a degraded service for CRM and since then it hasn't worked. I've also tried installing it on a different machine wirth teh same results.
I'm at the end of my tether as I can't roll this out in my organisation until I know it is reliable - at the moment its a damn nightmare!