Ok, I am going to run the risk of swimming against the crowd here.
I think we need to be careful of always blaming the client. I agree that you shouldn't change nails free of charge when the client has made the wrong decision, that goes without saying really. However, you said that you have many happy clients, which is fabulous, but then you go on to say that every few treatments you have someone with a problem. I think you need to look at these nails when the clients return and judge for yourself if they are maybe a little thin on the apex.
You are fairly new to the industry, and, even someone as old as me will sometimes slip up and make a nail too thin. I always have a look at the nails and point out to the client that the nail was thick enough where the breakage was or, if it was me, then I say so. That way I have built up a full book and waiting list of people who know I am always fair. If I get a silly one who complains all the time I get rid of them as they are never going to be happy and life is just too short.
You can learn a lot from really looking at these breakages, a lot about your clients and a lot about consistency in application.
Don't let it get you down though, this business can be the most wonderful thing. My longest job before this industry was about 3 years, I have been doing this now for nearly 18!