Most common reasons for Remote Desktop not responding?

• Connections being blocked by the local Windows firewall
• Connections being blocked by some other firewall device between your client and the server
• The server being behind a NAT arrangement that is not forwarding a port to the RDC port on the server
• The relevant service has stopped (manually or due to error)
• Remote Desktop not actually enabled (or was and has since been disabled)

If RDC was previously working then any of the above could still be the case due to reconfiguration.

When we were setting up a Windows 2008 server recently, we configured a bunch of network rules (including enabling RDC to be visible through the firewall for other local machines) before installing the latest service pack and other updates and for some reason the network settings were seemingly rolled back during the update process and had to be reconfigured. This has only happened once though, never on the other occasions we setup Windows 2008 in VMWare VMs, so it might be a red herring.

Out of Remote Desktop/Terminal Server License numbers. Remember Win2003/2008 license contains 2+1 admin connections. For more you have to license TS.

RPC freaking out is not uncommon.

There are some reasons listed in the answers to this question.