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.
Bitcoin price stability occurs because many people believe in the future of bitcoin. So they sell and buy in a balanced manner.
Because basically that when a coin gets an increasing demand factor it will be very good for the development of Bitcoin.