I am not a chemist so I cannot accurately say why verdigris appears but I believe it is a chemical reaction between the metal and the environment that it is in. Unfortunately the coins we like to collect are made of the metal that is the most likely to have this reaction, add to that moisture, bad storage and whatever else they react with and verdigris is one of the side effect.
like most chemical reaction if you can remove a part of that reaction it will stop.
If a coin has some verdigris on it and it is continuing to grow then the conditions for it to do so must still be present.
I have read that a small amount of baking soda will neutralise the reaction. If that is the case, and I have no way to prove it other than what I have read, then once it is stopped then as long as the other factors are controlled why should it grow again?