It is normal to expect learning to slow when new or more complex tasks are introduced. Landings are definitely complex, since they include many different tasks such as flying the airplane, talking on the radio, following traffic, performing pre-landing checks, and remembering to correct for wind drift. The main thing to remember is that a learning plateau is normal and does not mean learning has ceased - at least for most.
If my student has reached a learning plateau with their landings, there are a couple techniques I would try to help them overcome it. First, I think I would have them chair-fly the pattern to try to solidify some of the concepts that they need to grasp or that they are having trouble with. I would have them make sure they know the BCGUMPS checklist and know all of the airspeeds and power settings that work for each leg of the pattern. I would also have them practice talking on the radio while they chair-fly, so that when they get out to the pattern, it won't have them nervous or distracted from the real task at hand - flying the airplane.
Another option I think I would try is to stop working on landings for a lesson and do some other maneuvers that I know they are good at. The point here is to keep them from getting frustrated with the one task that they can't get down and focus on the things they are better at. This will alleviate some of their stress from the landings and also keep their confidence from taking a hit.
Finally, if after working with them for a few lessons and they still were having trouble, I might try having them fly with another instructor to gain another point of view. This may give them some new insights and the other instructor may say something to them that may make all the difference. Obviously, two points of view or opinions are better than one, and the more advice they can get, the better.
I think the point where I would tell my supervisor that they are struggling is when I send them up with another instructor. At this point, I think it is good for them to know in case the other instructor also has trouble helping them with their learning plateau. In that case, my supervisor would hopefully then be able to help with any further options for the student and/or myself and my teaching methods.
If the student still is having lots of trouble with landings after multiple flights with me and a flight or two with another instructor, I may have to sit down and have the "maybe aviation isn't for you" talk. Of course it isn't something I want to do, but it may be the best thing for them. It will safe them lots of money and effort to figure out sooner than later. It will also be best in the interest of safety. Landing is, of course, one of the phases of flight where the workload is highest and accidents most often happen. If my student isn't safe out there, it's bad news all around. Safety is the number one priority, and if a student doesn't have the skills to be safe, then it is definitely the better option to let them know that maybe they aren't suited for flying.
-TB
