First a student asks for an F-1 (sometimes J-1) visa. This can be delivered for a single entry (typical for Iranian students for instance), or for 1 or like 5 years (the common case for international students). The visa lets you _enter_ the country.
Once admitted in the US, a student can remain indefinitely while maintaining its student status (including school transfers). This applies to Chinese students as well. There is no renewal and if you only go to school or transfer school, nothing can really happen. There's nothing to renew every year.
The issue that arises is when a student leaves the US with an expired VISA. Then he has to apply for a new one before coming back. This is where it can get complicated. I have a student/friend who go stuck 4 months (in China) waiting to renew his VISA.