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.
Small miners would stop to mine if they find it no longer profitable to them to mine but not a big miners.. they look for a long term perspective and they can not stop mining. Because if they will stop digging, they will have more minus than long-term digging.