I guess the reason why bitcoin has a stable price is because miners are mining sometimes or even stop mining at all. The supply of coins freeze and the price would definitely freeze to. Correct me if im wrong but i really believe mining and the price are linked. If one stop moving then the other one will follow.
The market will never become stable, the price is always moving because it was depending on demand and supply, that is the reason why we should be always patient about the market prices.