coursepress hangs for certain users

We’ve run into a problem that seems to be specific to some students when taking courses. The problem is that after a student gets far into a course, the system completely hangs for any page requests that relate to courses, all other areas of the site work as expected. The hang ultimately produces a generic 503 error, or this message: Inactivity Timeout

Description: Too much time has passed without sending any data for document.

To help narrow things down, we tried this with a couple different student accounts and they all run into this problem after getting to about the same point in the course. The course we setup has 8 units and each unit has between 4 and 8 pages.

What else can we do to identify and fix this problem?