Maty Ezraty's reply:
Yoga has the potential to heal back problems, but it can also do the opposite: contribute to a back injury. I often ask, at the beginning of the class, who has injuries. I keep my eye on these students and look for ways that they may cause themselves injuries. Then I can try, in the context of the class, to advise and help them. Since your student has a recurring back problem, it is quite possible that he is doing something incorrectly in his practice.
I also try to ask the student how he got hurt. Sometimes a student hurts himself outside of class and needs to change that action or situation. He may also be suffering from old injuries that could benefit from a chiropractor, physical therapist, or other health practitioner. I am never shy about referring my students to professionals who could help.
If you are a new teacher, conducting the class and also taking care of someone who is hurt and in pain is a lot to ask of yourself. You may need to refer this student to a slower class or suggest a private lesson with an instructor qualified to help with his particular problem. When I was a newer teacher and was presented with this problem, I would try to go with the student to a more qualified teacher and learn what that teacher would recommend. I was never embarrassed to reveal that I did not know but wanted to learn.
The other approach is to spend time with this student after class. Give him a modified sequence that he can practice while in your class. The modifications can be small or large, depending on the student's needs. Not all teachers are comfortable with a student working differently in the back of the room, but this can and does work in many public classes.
If you are not confident in dealing with this injury, you should let your student know that he needs to seek another source of help. This is honest and will ultimately earn you his respect. As you develop your teaching skills, you will be able to work with similar students and still keep the rest of the class going. It does, however, take time and practice.
Maty Ezraty is co-creator of the first two Yoga Works yoga studios in Santa Monica, California. A former YJ asana columnist, she travels around the world leading teacher trainings, workshops, and yoga retreats.