After spending many, many hours on this, it looks to be when a student has submitted a PDF file as an upload that it causes the problem. I've confirmed this with a few more assignments and after removing the PDFs I was able to replicate the problem by re-uploading the files. Interestingly, the PDFs were made with Acrobat X and if I upload a PDF from years gone by, the problem doesn't exist?
To replicate, submit the attached two files as an assignment submission, attempt to grade the files with a feedback file. The page will break. Delete 'broken.pdf', and then try to re-grade. It will work this time.