Susiejean, do your students pay in advance? Do you ask for a deposit? I found using a combination of paying per month in advance and asking for a 4 lesson deposit, really puts me in a much better position. I too used to follow the PAYG method, and all to often people would cancel at short notice. After that I tried contracts and paying per half-term in advance. Again, I found people would stop, with no notice, and ignore any emails or texts. The number of times people would claim that they did not know about the notice period beggared belief. I once had somebody send me a cheque for my notice period, with a heartfelt apology for taking so long. That was a really pleasant surprise. Once, when using the PAYG method, a parent insisted I took payment for lesson cancelled due to the child's illness.
I have thought about this, and think people are often embarrassed to say that they are stopping or going to another teacher. I always emphasise to new students, I really do not mind if they move to another teacher, or decide the piano is not for them. Anyway, I found holding a 4 lesson deposit, means if someone stops with no notice, I still have a month's worth of payment. All lessons during term time are payable. The only exception I make is for adults who can take their holidays during the school term, on the proviso that any missed lessons are made up during the summer holidays. So far, with the adults, that works really well.
I do understand your dilemma, though, as I struggled with student number for a period of about 18 months. Not sure if this had anything to do with it, but things improved once a completely untrue review was removed from one website. My numbers have also really improved since I used Yell for advertising and for a new website.
In all honesty, most people are reasonable and fair. Just the occasional bozo or complete gimboid.