Just after I started private teaching, I fretted on occasion about the number of students I was maintaining at any given time. In the first month, I picked up 3 students then there seemed to be a pretty big swelling and I was up to 6 rather soon thereafter. Now, I currently have 8 regulars who attend once a week nearly every week and 3 "floaters" who schedule as needed (sometimes quite infrequently).
Lately, more have been canceling here and there than before because of various life issues and a sudden surge in travel abroad amongst them. I think that this is part of the natural "aging" process of the English learning experience. Early on, students are quite keen and tend to attend every lesson. As time goes by, they lose some of that energy and are more likely to cancel scheduled lessons for trivial matters or at the very least more likely not to allow the presence of a regular lesson to interfere with other possible appointments in the same time slot.
The most common reasons for early cancellations (that's the type I don't get paid for) are appointments with physicians, TOEIC tests, big social events and having to work late. As of late, I've been seeing enough scattered cancels to reduce my total number of lessons such that it's as if I had 1 to 1 1/2 fewer students and it was just starting to annoy me because I'm making $120-$180 less a month than I should be. That's a piddly amount of money to a full-time worker but not to someone in my shoes.
Anyway, just as I was looking at an income reduction, my former company tossed more freelance work my way and the referral agency I use to help me find students offered me one more student on Saturday. Of course, the new student might not work out. Sometimes students are keen to have a lesson and then they don't like how far they have to walk from the station or they decide to go with a cheaper lesson elsewhere.
Even though they know the situation before starting and get to pick their teacher from a small selection who meet their criteria, some will bug out after the first lesson for idiosyncratic reasons. In my case, I've lost one to having too long a walk from the train station (and it is a somewhat long walk), one to the referral agency's high rates, one for completely mysterious reasons (after an excellent first lesson, she vanished) and one who was apparently hoping for a girlfriend and didn't find me a suitable prospect. The latter fellow was an utter creep who sponged a half hour of free talk as part of a "demonstration" lesson with a number of teachers. He told me two previous teachers had taught him a few times and then asked the agency not to send him to them anymore so I probably wouldn't have accepted him with that track record anyway. I consider myself lucky to have only lost four so soon after the first lesson.
In language schools, you tend to experience "fade away" where students come for about 10 lessons and then lose interest and stop coming. I've only had one of those. Fortunately, I have had one-year anniversaries recently with the first three students who are still coming so I can say that most of my students have longevity.
In the past, I would have wondered if there was something wrong with me or my lessons when I lost a student, particularly after one lesson. I've come to learn that, while a student may reject a teacher, it rarely is anything the teacher is actually responsible for. I also would have felt depressed at the coming and going of students back when I first started and fretted about the loss of income but I can honestly say that karma has been kind to me since quitting my former job. When I lose one, either one isn't far behind or some freelance work helps me make up for the lost income.