Gradebook refuse to update fields in the database for response_types max_responses

Make sure for the assignment that you have selected a valid response type from the allowed response type list.

Also, check the dates for the assignment. If the assignment is past due then it won't appear in the list when the students try to submit a response.

Is a "create .... response" link showing when students view the assignment node?

Has the assignment already been graded? (I assume not, but this could also take the option to submit a response away, depending on your assignment and gradebook settings)

Have you restricted the number of responses to allow? Any chance the students are trying to submit more responses than the limit you have selected (set limit to 0 for no limit)

That's all I can think of right now...Hope this helps!