Copy the .brd and .sch file to your new files.
Make sure you have both .brd and .sch files open AT THE SAME TIME before adding components to the new .sch file. The new components should appear outside the board outline, but the scaffold components should stay where they are. It sounds like you're not opening the .BRD file, so EAGLE is creating a new one from your modified .SCH (and the component positions of the scaffold components aren't there, because it's new.)