Does Rogaine cause healthy good hair to fall out?

Monoxidil does not affect androgen insensitive hair (i.e. hair you were never meant to lose).It is important to remember that the gains made on medical therapy such as Minoxidil are dependent on continued use. Cessation in therapy will result either in resumption of losses or alternatively loss of gain.
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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Unfortunately William Rassman is incorrect. Minoxidil (the main drug in Rogaine) affects everyone differently.
While minoxidil works fine for the select few, the problem with the medicine is that it does not actually stop hair loss. Instead, DHT will continue is binding to the hair shaft which will eventually overtake any additional growth caused by the Minoxidil and die, perhaps just slightly later than it would have without the medicine.
Also, the alcohol base required to support the active ingredients also cause irritation of the scalp and severe reactions for many people, such as the increased shedding you are describing. The fact is that it does not work for everyone, and even if it does, not for long and not without side effects.
The number one first step I recommend is a comprehensive consultation with a hair regrowth specialist who will perform lab tests to determine the underlying cause of your thinning. Without labs, no-one can really know what your true cause is and any treatment will be temporary at best.
From here, you can receive the best treatment for your case.
Good luck on your search.

Rogaine (Monoxidil) was originally an antihypertensive drug that grows hair as a side effect. It will not impact normal hair