Some of the sheets were published after the app was published, some were not. None of those new sheets got copied over - and none of the new measures. I'm not sure whether it's possible to "publish" new measures or not.
Update: We were able to use a workaround mentioned in the following post:Howto add a published community sheet to the approved sheets. We did option 2: Copy the Binary File from the Apps folder, rename the Binary file with a .qvf extension, then import the renamed file.
This gave us a duplicated copy of the full app, including all new sheets and measures that were created after the app was published initially.
What I'm taking away from this is that we should never do development in a published app. When we publish an app we should immediately duplicate it back to My Work, then do any further development in that app.