Took too long to figure this out.  EagleCAD of course likes to keep the schematic and the board synchronized, and it won’t back annotate edits on the board into the schematic.  These are all happy, logical things that keep board designers sane.  However!  When it comes time to panelize or make multiple copies of a board layout for printing it won’t allow you to copy and paste sections of the board because it doesn’t want to perform the backannotation.

It took me a while of searching, but Keith’s Electronics Blog makes it sound like a cake-walk, it’s not that easy.  However, a random forum post gets it right:

Open your first file
Execute panelize.ulp
[It's in the top bar, icon with ulp in black text on a white "sheet of paper"]
Group
Cut (don't forget origin click)
Open your other file
Save as different file name
Execute panelize.ulp
Paste the other board in [the part you're trying to panel that you previously "cut"]

EagleCAD RS232 Driver Panelized