I think that there are a wide variety of techniques that you could employ in a situation like this. One of the best techniques that I can think of would be to ask a more experienced instructor for advice. They might be able to provide some fresh insight that you can use. If this doesn't help you could even ask the more experienced instructor to fly with your student for a lesson. This might help the student learn how to land in a new way that will click for them. You could also review the basic maneuvers used in the landing if you believe that the student is lacking understanding of a basic skill. These are just a few ideas of what may be helpful to both the instructor and the student, but I'm sure that there are a lot of ideas that are out there.
When to speak with a supervisor about the student will probably depend on the student. If you are on the 3rd lesson but you think that the student may just be getting it, one more lesson might help the student succeed. But if you are on the 3rd lesson and the student has absolutely no idea how to fix their landings, you should consider talking to a supervisor about it soon.
The "aviation might not be for you" conversation seems like it is definitely the last thing to do. I would probably have the talk after we have had multiple lessons where the student hasn't displayed any improvement. And even then I wouldn't have the conversation until I have had another instructor fly with the student. As a new instructor it seems like this is the worst possible conversation to have, but when it seems like the student will not be a safe pilot it has to be done.
