I know there is no forever but i think axie team are doing their best to prevent the game stable as much as possible. We can always see that axie could be gone but not anytime soon as the game getting more interesting as the dev unveils different progress of the gameplay. What rhey did on the increase of breeding fee is a way to preserve its price of those axies. They have a good niche on what to do, Im sure slp price or requirement on breeding will increase too later on and breeders can still do breesing even though its gonna increase later on since they love the breeding ecosystem of axie.

If this game will die, it would took many many years before it happened.