This might be a deliberate function, but here's the issue:
When you edit the permalink of a site, just under the Title-input, the "Get shortlink"-button disappears. It only comes back after you save the post.
I can understand that the "Get shortlink" needs the permalink-variable, but why not just send it to the button when "on blur" fires from the permalink-change?
Or is it that "Get Shortlink" only works when the URL is actually 100% and used in the system (as it is first after a save)?
Extra suggestion: remove the "Get shortlink"-button when entering Edit-mode for the permalink. It distracts a bit.