Sorry to return to this problem so late; but I had to gather more facts.
It seems that the students (and myself, sometimes) are logged off by either Moodle or TC.
We (in my univ) use an LDAP system. It issues a ticket (cookie) that allows the students to be recognised across the e-services of the university. This cookie allows to be instantly authenticated as we click on the login button of any univ e-service.
A student starts working on a task and takes a few minutes to complete it. When s/he clicks on "check", the HP activity returns a grade but Moodle, sends the studen to its front page and shows an unauthenticatded status (often after an error page saying "nodatabaseinfo" . If the student clicks on "login" immediatly, s/he is immidiately accepted, _via the cookie_ which shows it's still valid.
Further, TC says the current activity has been "abandoned" and shows 0% when the HP activity may have shown 100% justt prior to trying to get back to Moodle.
I asked the students to click on "check" more often, thinking that prolonged inactivity regarding moodle interaction might be the problem. It does not change anything. It just happens, from time to time.
Besides, relogging, prior to checking with HP, does not help. Moodle will not accept to register the HP result...
Have you heard of anything like this?
PS: Was very glad to read about you here. The article deserves some publicity!