I have tried every which way to get this to work, but every time I select every solid on my design and click Outer Shell, SketchUp has lost some of my solids in the process.

At first I thought it was stray guides causing it (because it popped up with an error stating that not everything I selected was a solid), so I deleted them. Same thing. I turned off hardware acceleration. I saved the result of Outer Shell to a new file, then reopened it to see if it wasn't just a display glitch, and it wasn't, these solids are really gone.

I'm posting links to my files on Google Drive, to see if this file does the same thing for anyone else:

https://drive.google.com/file/d/0B0SzaHgNql5XZnl3bEN6a1NiNzg/edit?usp=sharing

https://drive.google.com/file/d/0B0SzaHgNql5XWXBNeGF0RFptXzQ/edit?usp=sharing