If a student demonstrates in some way that they will never be "airworthy" I think it's our duty to see that they don't be given the ability to hurt themselves and others (us!)
Disguise Delimit's tale show's why just ceasing flying with a student (although it's often our only choice, and I've done it too) will not always stop that student achieving their "dream" through force of $$$. If we're really concerned, we may need to persue something like the following...
The wording in the following is a little strong (i.e. "phychological abnormality"), but I think the sentiment of the passage relates to the matter at hand.
From the FAA Aviation Instructor's Handbook
FLIGHT INSTRUCTOR ACTIONS
REGARDING SERIOUSLY ABNORMAL STUDENTS
A flight instructor who believes a student may be suffering from a serious psychological abnormality has a responsibility to refrain from certifying that
student. In addition, a flight instructor has the personal responsibility of assuring that such a person does not continue flight training or become certificated as a pilot. To accomplish this, the following steps are available: 2-6
• If an instructor believes that a student may have a disqualifying psychological defect, arrangements should be made for another instructor, who is not acquainted with the student, to conduct an evaluation
flight. After the flight, the two instructors should confer to determine whether they agree that further investigation or action is justified.
• An informal discussion should be initiated with the local Flight Standards District Office (FSDO), suggesting that the student may be able to meet the
skill standards, but may be unsafe psychologically. This action should be taken as soon as a question arises regarding the student’s fitness. It should not be delayed until the student feels competent to solo.
• A discussion should be held with a local aviation medical examiner (AME), preferably the one who issued the student’s medical certificate, to obtain
advice and to decide on the possibility of further examination of the student.
The flight instructor’s primary legal responsibility concerns the decision whether to certify the student to be competent for solo flight operations, or to make a recommendation for the practical test leading to certification
as a pilot. If, after consultation with an unbiased instructor, the FSDO, and the AME, the instructor believes that the student suffers a serious psychological deficiency, such authorizations and recommendations must be withheld.