After you have saved to the clipboard, are you then visiting a new individual? If staying on the same individual you will need to refresh the screen.
I have just tried it on my site and it works OK.
The code for all is in a single place, so there is no logical reason I can think of yet why it would work for birth and not residence.
The other possibility I might guess at is that you are looking to copy from the clipboard to a family record. This is not possible. Clipboard can only work between individuals.