Why would eyebrows not grow back ? and just fall out in their own ?

Thyroid: Loss of eyebrow hair can be caused by an underactive thyroid or autoimmune disorder. When eyebrows are shaved they may not grow back. For further evaluation see your pcp who can order appropriate tests.

Telogen effluvium: Eye brow hairs can thin just like hair loss with age. Hertzoge's sign is loss of hair on the outer 1/3rd of the eye brow. Sometimes this condition may be associated with hypothyroid condition. Alopecia areata is an autoimmune condition where the patients own aintibodies attack their own hair follicles. My recommendation would be to see your local dermatologist or consult your local medical school.

Grows slowly: Eye brow hair grows very slowly and thus the misconception that they won't grow back after having been shaven. If you have not plug the hair out in the first place, then you need to see a dermatologist to find out why you are losing your eyebrow hair. If you have shaven it off, it may take many months to recover.