Can a college player lose his scholarship just for playing badly?

Yes Very much indeed. Coaches threat their players about it. If you dont play good they can revoke your scholarship. You cannot get it taken away if you get injured though.

Yes. Depending on the school, a student-athlete can have his or her scholarship revoked for any reason. In major athletics, such as football, this is more common in the largest of schools (such as the University of Alabama, coached by Nick Saban), who are also notorious for oversigning athletes. Many fans consider this unethical and repulsive.

Yes, in rare cases. Or if what he does is really bad he could be kicked off the team or out of the university.