MDL-38538 implemented server-side auto-save for the quiz. That is very good, but only while you have a working connection to the server.
It might be possible to sue the DOM Storage API (https://developer.mozilla.org/en-US/docs/DOM/Storage) to implement client-side auto-save in the quiz as well.
We need new JavaScript code mod/quiz/yui/autosave/autosave.js, which notices any time the contents of any form field (or TinyMCE) inside the quiz responses form changes value, and then does a callback a few seconds later to save the values.
Later, if the quiz page reloads, we check the DOM storage, and if there is data there different from the most recent value stored on the server, then we update the form fields with the saved data.