Have you ever had copy and paste give out on you during the day in one or all of your rdp windows? If so there is an easy solutions to get it working again. Basically the copy/paste over rdp process has crashed on you.
Just bring up task manager on the target (the one you are remoted into) system and look for the process rdclip and end task on it– they system will then auto-restart the process in that background the next time you try to cut/paste and the feature will function again.