If I use Rogaine and stop using it, will I lose all hair on the scalp it has touched?

It is important to remember that gains made while using medical therapy such as Minoxidil are dependent upon continued use. Cessation of therapy is typically associated with some loss.
With regards to your specific, the cessation of medical therapy is often accompanied by the loss of the gains which are attributed to this therapy. However, the losses are typically limited to the gains made during long term usage (4-6 months). This is due to the fact that it takes some time for the development of new growth which is medication dependent.With regards to your specific question, cessation of therapy will typically affect hairs that were being preserved or regrew secondary to therapy.
As always, discuss your concerns with a board certified plastic surgeon (ABPS) with experience in hair restoration.Donovan Rosas MD
Board Certified by the American Board of Plastic Surgery
Member: American Society for Aesthetic Plastic Surgery, American Society of Plastic Surgeons
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Hello and thank you for your question, certainly by using Minoxidil any of those roots which are still alive could regrow hair and you may find visible difference, however if you happen to stop using minoxidil and as those roots are dependent on it, they will start shedding and you may lose them for good. Ideally as there are not many solutions in order to stop your hair loss and regrow hair, you could use minoxidil and may continue to use about 1ml / day for at least 12-18 months in order to enjoy your natural growing hair for longer than if you never use minoxidil. 

If you have hair that was grown by minoxidil and then you withdraw the minoxidil, then you will loose those hairs that were grown by minoxidil which will be dependent upon the drug