I'm tutoring a student. Unfortunately he's not very good; for example, he has trouble with basic manipulations that one would expect a student of his level to have mastered. He scored 15% in a recent test, and that was a lucky score, since some of those points came from multiple-choice questions that he guessed correctly.
I don't believe he's beyond saving, but any rescue would have to involve close oversight and substantially more time spent studying, i.e., more classes. Furthermore, if one were going to attempt a rescue, then the rescuer had better start as soon as possible since the student's lecturer will be moving on to new material and not waiting for him to catch up.
However, if I recommend this to him/his parents, then I am indirectly recommending they hire me for more classes. This sounds like a conflict of interest. I could say "hire another tutor", but this looks artificial because from the point of view of the student, it's obviously better to work with the tutor who already knows you. Can I ethically recommend the student take more classes?
Related: Is it ethical to profit by having my students buy my textbook? which also deals with the teacher recommending students do something that benefits them financially.