One method that I would use to get the student over the learning plateau is giving them a break from the landings. To do this I would bring them back to the ground reference maneuvers and similar basic maneuvers that they have already mastered and show them how they apply to landing. I think that this would help not only to give them a break but to also build their confidence. Another technique is to have them make low approaches and fly in ground effect without landing. This will help to make them more comfortable with being close to the ground and get them used to the feel of the controls that close to the ground. I may also make a few landings myself with the student feeling the controls along with me to get a better idea of what should be done and when it should be done.
As for when to talk to a supervisor, I would probably do so after completing lesson 8 three times. If at the completion of the third lesson it is obvious that the student is making no progresss then I would talk with a supervisor and probably ask them if it is okay if another instructor tries to teach the lesson to them, for it could just be the way that I, as the instructor am trying to teach it.
The "maybe aviation isn't for you talk" seems to be a difficult one to put a number on, for it seems to depend a lot on the student and how they feel about their flying and progress. For example if the student doesn't seem to be that into flying and it is obvious that they are not getting a hold on landing than I may make the talk a lesson or so earlier. But if the student is really motivated to learn and loves to fly then I may give the student one more lesson before making the talk. But as a number I feel that about 5 repeated lessons with no improvement in sight would probably be about the time to make the talk. However before I did this I would send the student up with another instructor to get a second opinion on the situation.
