How long until a hair follicle becomes dormant?

There is no exact amount of time as hair loss and follicular health is related to individual biology, genetics, and age.  That said, most often evidenced from under a scope to detect microscopic growth, it varies between the crown and the frontal hairline.

Hair loss in the temporal areas are the most resistant to regrowth as is also the amount of time they can be re engaged.   Most estimates will put that area at about 2 years. (For some as much as 5 years)  

That said, the younger you are when you start treatment, the better the outcome.  For the crown, a good estimation is as much as 5-10 years.  Beyond this, most hair growth options are designed to maintain the rest of the hair left and further mature them to allow them to be as dense as possible. 

As with all hair growth strategies, early detection of hair loss and early treatment always lead to the best prognosis.  With that in mind, however, many people with advanced hairloss have been able to resuscitate enough terminal (fully matured) hairs to make a dramatic cosmetic difference.