Unfortunately for them, Chinese teachers must undergo annual medicals. That is in my view unnecessary. They aren't airline pilots, after all! As for foreign teachers, they are generally not forced to undergo annual medicals so long as they do not change jobs.

I used to be a secondary school teacher in the UK. There I only had to have one medical exam during ten years of teaching, and that was after graduating from a college of education in order to be registered provisionally with the GTC. That meant I was licensed to teach. After I had completed my 2 years probation successfully, I received full registration.
In my first 6 years of teaching legally in China, I had no medicals. But I had one in the UK before coming to China. The college FAO in my first job tried to force me to take a Chinese medical some four weeks after my arrival, and after I had taught without a Residence Permit for three weeks, at which time they offered me a teaching contract. Of course, I had no idea of this illegal and wily procedure when I applied for my Z visa for China back in the UK before coming to China. - I flatly refused to take another medical, and so did my former wife, who was with me at that time and employed as a foreign teacher by the college too. We completed our two-year contracts at that college, and moved on to another part of China to continue our teaching careers.