I had this same issue. After verifying the Windows Firewall was disabled, I started to check the log file located in C:\Users\<username>\AppData\Roaming\Mitel\UC\ucc.log. In review of the log compared to a good working system, I found the issue to be caused by a virtual OS adapter being bridged with the internal NIC adapter. Initially, you will need to break this bridge and restart the UCA Desktop Client. After the initial client setup, you may recreate the bridge. Also, make sure that no adapter uses the same network connection that your MAS server and UCA Server. This may affect your issue too. I have tested on the 2 affected systems and it worked just fine.
2013-01-04 14:14:44.407 Msg [MainThread]: FastBootManager: Booting Web Services Service
2013-01-04 14:14:44.412 Msg [MainThread]: NetworkMonitoringAgent: Network Address Changed!!!
2013-01-04 14:14:44.416 Inf [MainThread]: NetworkMonitoringAgent: Existing Network Adapter: TeamViewer VPN Adapter, IP=0.0.0.0, IfIndex=19, MAC=00ff25767957
2013-01-04 14:14:44.416 Inf [MainThread]: NetworkMonitoringAgent: Existing Network Adapter: MAC Bridge Miniport, IP=172.x.x.x, IfIndex=15, MAC=xxxxxxxxxxxxx
2013-01-04 14:14:44.416 Inf [MainThread]: NetworkMonitoringAgent: Existing Network Adapter: VirtualBox Host-Only Ethernet Adapter #2, IP=192.168.x.x, IfIndex=18, MAC=xxxxxxxxxxxxx
2013-01-04 14:14:44.416 Msg [MainThread]: NetworkMonitoringAgent: Network adapter added: MAC Bridge Miniport, IP=172.x.x.x, IfIndex=15, MAC=xxxxxxxxxxxxx
2013-01-04 14:14:44.416 Msg [MainThread]: NetworkMonitoringAgent: Network adapter added: VirtualBox Host-Only Ethernet Adapter #2, IP=192.168.x.x, IfIndex=18, MAC=xxxxxxxxxxxxx