Yes you have to do it every time you renew the residence permit. They take that health issue thing seriously. If you stay here one year that's fine you've already done it. WHo knows what people do within that year. So yes it is required to renew it once a year or every time you want to renew. 

The requirement varies from province to province. In some provinces (e.g. Inner Mongolia unless changed since I was there), it is an absolute requirement. In Shandong where I am now, they do not require the check to be carried out every year. It is one of those grey areas that is applied differently according to region.

There is not question of time for Medical exam. When School applies for extension of RP, PSB will (or will not, depend on the Province) ask for Medical Exam certificate. 

You will receive Medical certificate in few days after check-up, and usually School pick-up the bill, if you pass the exam.

I had to do Medical exam last September in Hong Kong, and I had to do it again this year in June for new RP extension in Xinjiang.

I was in the same school for the last 2 years, and had to get the health check before the start of the first semester each time. Now, because i am changing provinces, i have to get it again: it appears to be a standard requirement for most types of employment.

Only once here as well... I'm in (too) sunny Fujian 

In Hebei, you have to do it every year. I was there three years.

I've only had to do it the first time.  I've had 2 annual renewals thus far and neither required a health exam.  I'm in Zhejiang province.

Yes, and it includes anal probing.