Hi again, Christabel. With regard to lessons with knowledge check blocks, here's my understanding: if the learner suspends the course while inside the lesson with partially answered Knowledge Check questions, it is expected behavior that the learner will resume at the beginning of that lesson and their responses will not be saved. However, if the learner suspends the course after they've completed a lesson and answered all Knowledge Check questions, their answers should be saved. So, to summarize, if you stop in the middle of a lesson, you lose progress in the lesson, which includes entered responses. This logic would also apply to quizzes as I understand it.
If I'm not correctly interpreting the issue you're seeing, or if you'd just like someone here to take a closer look at this, let me know and I'll open up a support case on your behalf.