Using Mac OS X 12.6.8 and Remote Desktop 10.9.2. Beginning two versions back (10.9.0?), copy and paste works for a while after launching RD, but it eventually fails when copying from the remote mach...
This is still happening.
But what I have realised is that pasting the copied content first on to TextPad and then copying the content from TextPad never fails (make sure you're using the ⌘+c and ⌘+v).
Hopefully you should not get the beachball of death.
So it must be application related rather than Remote Desktop.