Well, you just have to keep trying. Even the most popular schools do have vacancies from time to time, as expats and their families come to the end of their contracts and move on. Sometimes information on school websites has passed its "sell by" date and the school is going to open a new school building, so that tere WILL be some empty places.

I am surprised that more parents do not start their own schools. If you are going to do homeschooling, why not have a few more children in the class?