Well, finding nothing in the logs is always a worrying situation to be in. There are two possible explanations for that: Either there really are no errors, or you did the wrong search. It is nice if you can verify which of those situations you are in, just to be sure.
What you should see in the apache logs during a quiz attempt is a sequences of GETs of mod/quiz/attempt.php which return a 200 OK, alternating with POSTs to mod/quiz/processattempt.php which return a 30X redirect back to attempt.php. So, make sure you see that at the expected time. (And no redirects to login/index.php from the same IP address other than the initial login). There should probably also be some calls to mod/quiz/autosave.ajax
.php in there.
Basically, before you risk making a false accusation that an honest student is lying, you have to be very very sure you understand what you are seeing in the logs. Can be good to log in to the quiz yourself, and attemtp it as teacher (preview) so you can be absolutely sure what a 'normal' quiz attempt looks like in the logs, for comparison.