You may notice that your clipboard will sometimes work over RDP(TS) sessions, but sometimes not.
Normally the problem is that the server has clipboard access disabled.
Just follow these instructions to enable it
1. Log into the TS (on an account that has administrator rights)
2. Run the Terminal Services Configuration program
3. Select the Connections folder (under Terminal Services Configuration on the left window pane)
4. Right-click on the RDP-tcp connection (in the right window pane) and select Properties.
5. Click the Client Setting tab
6. Un-tick the Clipboard Mapping option under the Disable the following: heading.