Tim Hunt has made some major progress in the realm of Autosaving student examination sessions and displaying any connectivity issues to the student if the connection does happen to drop. Autosave of a quiz actually has been available since Moodle 2.5’s release [http://docs.moodle.org/25/en/Quiz_settings#Site_administration_settings] but it has not displayed whether or not the active session is still connected. Tim’s worked to correct that and display relevant information to the student/user in the case that internet goes out.
Catch up on the full discussion with mockups and screenshots here: https://moodle.org/mod/forum/discuss.php?d=243638
Follow the tracker ticket to stay up on progress here: https://tracker.moodle.org/browse/MDL-42504