Have grey beard. Hair start falling .... ???

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Have grey beard. Hair start falling if it grows beyond a certain length. No skin problem. What should I do ? The options of shaving or reducing the beard size are out of question. The options of shaving or reducing the beard size are out of question. At present hair length of my beard is seven inches. This is not a new problem. Whenever the hair length exceeds five inches, the problem starts. I have wavy hair, if that is any help.