I think I have a clue to the problem. I pulled this site from Multisite into a standalone WordPress installation. During that process I backed up my mysql database. When running mysqldump this error appeared: #1286 - Unknown storage engine 'InnoDB'
I didn't notice any other problems with WordPress. An InnoDB failure seems to make the quiz questions disappear. I restarted mysql, the error went away and the quizzes appeared again.