It depends, if the student in question is really dangerous and makes serious absolutely unpredictables mistakes, I quit. I had one student who made the strangest cockups, I kept on going let other instructors fly with him, but we all had to conclude we where really feeling unsafe and he didn't seem to have the talent. At the fourth attempt to kill us both, I quit.
He went on with other instructors and finally after a lot of hours got his licence. So maybe I should have continued and make the money.
As said before stage checks are really important, and if somebody is unsuitable I don't want the responsibility to send him solo.