What discipline you show in, and what association, changes how much losing amateur status affects you. Some disciplines have classes and divisions specifically for amateurs and specifically for professionals.
I turned professional when I was riding hunters, and it made absolutely no difference to me at all. I hadn't been showing in the Amateur Owner divisions before I turned professional, so I didn't much care about not being able to show in them after.
Most disciplines have "Open" divisions for amateur and pro alike.
In AQHA you can't have amateur status if you receive horse related compensation within the previous 5 years.
The rule reads:
You may obtain an amateur membership if you have not shown, judged, trained or assisted in training a horse (whether or not a registered American Quarter Horse) for remuneration, monetary or otherwise, either directly or indirectly, nor received remuneration for instructing another person in riding, driving, training or showing a horse for five calendar years previous to application for Amateur membership.
As soon as you start taking money for training or lessons, you become a professional. If your expertise is such that people will pay for it, you are no longer an amateur and can no longer show as such.
Amateur/non-pro rules exist to help level the playing field, so that amateur riders have classes where they can compete without worry that pro trainers are going to come in and clean up. There are some that use this to their advantage and are really more like "professional amateurs", but in general, it tends to work.