I pretty much agree with the other posters. If I didn't feel like I was getting anything from the private school, then I would switch schools as well. Also, I would pull privileges until he gets the grades back up. That means no cell phone or telephone, no tv & internet, and no hanging out with friends on school nights (weekends maybe) until grades are up. How's that for motivation? Even after he gets the grades up, I would not allow the phone, internet, or tv until after school work.
On a side note, I know the teachers think he is capable, but does your son think he is capable? Maybe he just got overwhelmed and now he thinks he can longer do the work, is this possible perhaps? The school you are sending him to sounds very hard. I mean, Chinese in eighth grade? I'd fail that too! Even if he is capable, if he does not believe he is, then he has already defeated himself.