To save the area to the clipboard, I have the default key combination Shift+Ctrl+Printscreen. Then I cut the area, but there is nothing in the clipboard (check via Ctrl+V). It happened a week ago.
I'm afraid we broke that in the last Gala release when we tried to remove a lag / freeze when making screenshots (See: PR).
We've solved the issue and it should be fixed with the next release of Gala.
Update: A new version of Gala was released which should include the fix: