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.
I kinda disagree with what you said. I do believe mining somehow have effect on the prices but.. miners does not stop mining and the supply never freezes, remember bitcoin have a constant supply in every blocked solved until it halved. It will take another century for Bitcoin to stop giving reward.
I think bitcoin price is tanking because of several reasons and one of which is the adoption of every country, the legalities issue that if approved will boost the people getting in to Bitcoin. So in short, it is not the miners but rather the adoption of people. Remember market price is driven by supply and demand.