That is odd! I haven't noticed this problem. I was too busy working on some important stuff. I have recently heard that people had to pay for going to highschool and also I know people have to pay for going to training centers no matter what age you are. If your talking about training centers they probably just don't want to go anymore. 

A Chinese teacher once mentioned that every Tuesday is a half day for teacher institution day (that's what we called it in America, basically training).  At my old high school we had late starts, where students came in 2 hours later every 3rd Tuesday.  Anyone more knowledgeable can confirm or deny this?

They could be the children of migrant workers.  If they aren't official residents of that area, they won't be allowed in the formal schools. 

I would have to say Lina90's post is probably your best bet. The children don't have the local hukou, so they might not be able to register. There are also poor families who need their children's help. That's more likely to be a girl, if she has a brother, they can only afford to send one child to school. Some kids just drop out of school, maybe their parents don't care. Also, if they're old enough to be in high school, maybe they didn't get a good enough grade to go to high school. Or they could just be skipping. Who knows.