One of the main factors implicated in hair-loss is DiHydroTestosterone (DHT), which is a steroid that is roughly three times as potent as regular testosterone. It is synthesized from regular testosterone by an enzyme called 5-alpha reductase. High amounts of naturally occurring DHT drive so-called "male pattern baldness". Excessively low natural levels during gestation and youth can result in certain intersex conditions.
DHT contributes to hair loss by building up in the follicles and reducing their viability. At first, the follicles just slow down and gradually become dormant. However, follicles that are exposed to DHT for a long enough time will die. Oral meds for controlling hair-loss typically work by blocking the conversion of testosterone to DHT.
In transwomen, the HRT given to promote development of feminine secondary characteristics drives testosterone levels down to the "female normal" range (even ciswomen need a small amount of T) which makes much less T available for conversion to DHT, so the hair meds may be less necessary. Orchi or full SRS makes the hair meds mostly unnecessary by removing the testes; a primary site of T production and DHT conversion.
Men using either Minox or oral hair-loss meds are usually advised that the hair loss will resume if the meds are discontinued. Also, revived hair is often finer and somewhat more sparse than it was before the hair loss began.
One happy side effect of driving down your DHT levels is that it may also reduce your likelihood of prostate cancer. On the other hand, DHT blockers (5-alpha reductase inhibitors) may somewhat elevate your risk of breast cancer. You win some, you lose some.
DHT blockers do carry a risk of side effects such as impotence and/or diminished libido. For many of us girls, that's not really much of a worry, but it is something to be aware of.
You should talk to your doctor before starting or quitting hair meds to be sure there is no conflict with everything else that is happening with your body.
I'm not quite clear on exactly how Minoxydil works, but I suspect it acts topically (from the outside in) to block DHT from reaching the follicles. This would necessarily make it less effective than the many oral meds on the market. Some people experience temporary shedding after starting Minox; this is discussed in the documentation that accompanies the stuff.
Keep in mind that while dormant follicles can be stimulated into growing again this way, truly dead follicles cannot be brought back. If the meds do not restore the hair satisfactorily, other options must be considered.
I've been using minox by itself for several years and have had some slow success with it, but I suspect it would work better in conjunction with oral meds, such as Avodart or Propecia.
That is all the long way of saying, "As a transwoman, you may be able to discontinue after HRT or surgery as advised by your doctor. If the hair loss resumes, you can always start using it again. For men, it's usually a lifetime prospect."
I hope that all made sense.