This is an annoying issue I ran into today with remote desktop and windows.  I use remote desktop to get to my other computer at work and without the copy paste function it is a huge hassle.  I found another blog that ran into the same issue to solve this issue:

Go to the remote computer, run taskmgr.exe then end the process rdpclip.exe then go to run and re-start the rdpclip.exe process.