This looks like standard network errors. I'd suggest launching Terminal (Utilities folder) and typing in:
'telnet ServerIPAddress 3389' (e.g. 'telnet 10.10.10.10 3389') alternatively you can use the server's domain name such as 'telnet myservername.com 3389'
After typing the above and pressing 'Enter', if the connection is working you should get something in Terminal like:
Connected to ServerName
Escape character is '^]'.
This will confirm that the network setup is correct and firewalls are allowing traffic through. To return to the Terminal prompt type:
This will result in a prompt of 'telnet>'
Then type quit, which will return you to Terminal's command prompt
If you get the above results, then double check the server address in Remote Desktop Connection before clicking 'Connect'
If Terminal hangs with a 'Trying ServerIPAddress...'
telnet: connect to address ServerIPAddress: Operation timed out
telnet: Unable to connect to remote host
Then there is a basic networking problem that could be caused by your network, the remote network (you haven't mentioned whether these Terminal servers are on your local network or a remote network) or the configuration of the Windows server. The most likely causes are:
Change of Terminal Server IP address
A firewall restriction on a network or the server
Change of the standard 3389 TCP port on the servers
Change of NAT (network address translation) rules on a router/firewall
I'd recommend contacting the administrators of these Terminal Servers and their networks and asking some of the above questions.
I hope this helps