I recently have had two cases where a portion of a PDF file that I saw on screen didn't print. Both documents had inserted signatures among other things. When I opened the file in Acrobat and Illustrator, I could see there were multiple objects. It was some of the objects that were not printing. I figured I should be able to solve with Illustrator, but never came up with a solution using it.
Back in Acrobat, I saved the PDF as a Word document. Then from Word, I created a new PDF. Now my new PDF was complete and it printed everything that I saw on the screen.