If you catch the system locked up again, try connecting directly to the webwork service via http://webwork.yourschool.edu:8080/webwork2. Depending on your firewall rules you might not be able to access this from a browser, so from the command line via ssh you can try
curl http://localhost:8080/webwork2
If that returns the html of the webwork landing page, then the webwork service is running properly and the problem is likely somewhere else.
Also check the status of the apache2 service, and try restarting it. It's possible that apache is the thing that crashed and not WeBWorK.
The other thing to check is that the disk is not full, though if this were the case I would expect that you would be seeing other symptoms as well.