What can cause a 16 years old child to stop menstruating, she is not pregnant as that has been tested and came back negative, its been 4 months now?

Many causes. Missed periods can be caused by stress, increased exercise/athletics, or sudden changes in weight. Sometimes the problem can be more serious and may require hormonal evaluation. I would take her to her doctor.
Unpredictable Period. Having ruled out pregnancy the other possibility is that adolescents will typically have irregular periods when they first have their periods. Other possible causes are medications or an underactive thyroid.
Menses. Get yourself tested for poly cystic ovarian syndrome as it a common cause in your age group.