It sounds like cookies are not being set.
In /opt/webwork/webwork2/conf/localOverrides.conf around line 503, do you have $session_management_via = "key" commented out? If so then you are using the default of session management via cookies. You could try uncommenting that line and see if that fixes the problem.
Alternately check the variable $server_root_url in /opt/webwork/webwork2/conf/localOverrides.conf. If you are serving via a proxy, then you will need that to be set to the url of the proxy.