Site Admin -> Server -> Session Handling.
Default is 2 hrs ... can be increased to 3 or 4 hours. Also recommend setting a cookie prefix. Students could be asked then to find that cookie in their browser to assist in troubleshooting issues they might be having should it be needed. Also ... using DB for sessions? (on the same form) Default is no. If checked (ie, it's on) consider turning it off and use file based sessions.
There could be issues with connectivity ... which wouldn't report any error to students. That sort of issue is beyond the control of the server upon which Moodle resides and maybe beyond the control of the network upon which the moodle server resides.
Is there a way to provide students a look at the assignment objective in advance of clicking the actual assignment activity?
'spirit of sharing', Ken