Typically high schools are based on credits for students. If a student has earned those credits, I suspect the school would discourage repeating a year. If a student made a C or lower in a math or foreign language class, perhaps they would allow this student to retake one or two classes, since subsequent, more advanced classes need the more basic skills for one to be successful.

To answer your question more specifically, call the student's high school principal or school counselor for their recommendations based upon their knowledge of this particular student.

Hi Krislyn,
   I'm sorry to hear that this student of yours is struggling in the classroom and with his/her confidence! To my knowledge its legal for a parent to make an agreement with the school,teachers,student, etc. and repeat a year if such an agreement can be reached, however if this is your child we are talking about always make sure to consider other options as well.
 Research has shown grade retention (repeating a year) can often hinder a student's academic future. This isn't to say that all students have the same results however when staying back a year!
If this student does decide to stay back a year, make sure he/she does so with a complete and comprehensive plan on how to succeed in the coming year, otherwise it will simply be a year of the same challenges which can be demoralizing to many if immediate progress isn't seen.

Here is a good article on the debate of grade retention to get you filled in.

http://www.education.com/magazine/article/Should_Struggling_Students/

Hope this is helpful!
-Alex