I earn a living as a private tutor, going from house to house like a door-to-door salesman, peddling knowledge instead of vacuum cleaners. I suspect that some of my wealthy clients put me in the same category as their lawn cutter - I'm the guy who shows up once a week and delivers a service they pay for. See you next week.
It's true there is some deep appreciation here and there, particularly when you save a student from failing an exam, or better yet, when you manage, during an extended period of time, to raise a student's grade from a C to a B, or perhaps even to an A. One frustrating aspect of tutoring is that you never know which new student is going to end up benefitting from the sessions, and by how much. It all seems outside of your control somehow, and an honest tutor must admit there is no magic formula.
With a very small percentage of students, tutoring doesn't work and the parents realize they are wasting their money. That happened recently with a student who needed homework help due to surgery that kept her out of school. I tutored her just a small number of times, perhaps four or five sessions. The girl went back to school and got a 66 on a chemistry test, after which the mother emailed me saying they wouldn't be needing my services anymore. There is no way to know what went wrong, since you never get to see the exam. You've been fired without an opportunity to address grievances. Could the girl's poor test score have resulted, in part, from the fact that she was spaced out on Percocet (a pain killer required after her surgery) for the first couple of sessions? I've had students tell me to help them prepare for a test on one topic, then go to school and take an exam on some other topic because they had gotten it wrong. Who can say what happened with this particular student, but there was no second chance, and it bothers you from a professional point of view that you've got this parent out there thinking you're a bad tutor.
For the overwhelming majority of students, there are solid gains to be enjoyed from private tutoring (the same can be said for online tutoring, by the way; see the 24HourAnswers.com blog article Online Tutoring Is Good - As Long As It Mimics Offline Tutoring). Test scores normally start improving after a few sessions, typically scheduled once each week to fit homework patterns, test schedules, and parental budget constraints. Normally there is an improvement of one full letter grade, which in turn leads to increased confidence that allows the student to enjoy the subject more, all of which contributes to a cycle of enhanced learning.
At the other extreme, there are a very small percentage of students whom you just happen to meet when the time, place, subject being studied, and attitude all coalesce to produce dramatic results that astound everyone involved. An example of this happened when I first started private tutoring with a kid who had been failing math since the beginning of the year. Fortunately, the parents intervened early, and I began working with him sometime in November. Although the student was not particularly bright, he devoted himself 100% to our sessions, and little by little, week by week, his grades steadily improved. After about five months, his grades had reached the 90s and the student began feeling he didn't need me anymore. When a student has improved so much that he feels you are no longer needed, you know you've done your job as a tutor.
I wish I had more control over the outcomes of my students, but I'd be dishonest with parents if I told them I could guarantee a good result. Fortunately, if the student is diligent and patient, good things almost always follow from time spent with a competent tutor. If that weren't the case, we tutors would look for something else to do.