There are many potential reasons for connection issues or connection drops. This is a list of the most common connection issues, with suggestions on how to solve them.

Buggy or old drivers

Strangely enough, out of date graphics drivers or network card drivers on the server that's hosting the RDP session can cause issues. This is the first and simplest thing to check -- make sure your graphics and network drivers are up to date on the server.

Connections blocked by the local Windows firewall

Sometimes the RDP service can be disabled, but the port blocked on the Windows firewall. To solve this, open port 3389 in Windows firewall.

Connections blocked by some other firewall device between your client and the server

If you have other firewalls on your network, check them to ensure that port 3389 is open.

NAT not forwarding the RDC port

If your server is behind a Network Address Translation (NAT) device, ensure that the NAT is forwarding port 3389 to your server.

Remote Desktop Services service is stopped or disabled

To solve this, open the Services Administrative Tools item and start the Remote Desktop Services service.

Remote Desktop isn't enabled, or it was but has been disabled

If all else fails, double check to make sure that remote desktop is in fact enabled on the machine. If not enable it. If you don't have physical access to the machine, you can follow the Remotely Enable Remote Desktop guide to enable it from a remote machine.