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.
We can see thousands of transaction that is happening everyday and definitely a complete transaction. Mining never stops and I doubts this is the cause of the stable price. Preferably by now, you heard about this correction which I think could be one of the many reasons why it was stable for a couple of months.