You can find that if you go to the assignment grading area, and uncheck the Quick Grading checkbox there (this needs to be done by user individually).
Another thing that can happen: instructor would grade in that pop-up, and then do not save there by clicking Save Changes button in that pop-up, but instead clicks on the Submit All my feedback button at the bottom of the assignment grading page.
Then the feedback will get lost.
But then you said that he does indeed clicks on Save changes, but the info is simply not getting transferred.
(therefore once he clicks Submit All, there is really nothing to save).
I believe that is some kind of bug with the assignment tool.
I would probably ask in the assignment forum
Gradebook
Grade book not updating for every student in course
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