The requirement that students study full time is one that was brought in around 2014. The department treats all designated learning institutions the same, as far as that requirement goes. For post-graduate work permits, which is the ability to work in Canada after graduating, students have to have studied full time.
There's little sympathy given right now to students who may have to study part time because of family needs or mental health issues. The big issue that arises is that to get a post-graduate work permit, a student must have studied full time in every semester except for the final semester. It's always been a bit unfair to students who, say, study part time in one semester of year two of a four-year degree, for whatever reason. Those students will not be able to stay in Canada to work after graduating, while those who study full time, except for the last semester, can.
It's something I'd like to see changed.