It will never stabilize, and you summarize why pretty well with this post. The Bitcoin price will continue to rally and then crash forever. When people think it will go down they will sell, hoping to get cheaper coins later, which pushed the price down. Then, when it has fallen so far that enough people think it can't fall much further it stop falling.
That's a really silly statement. If Bitcoin remained "forever volatile" you would see hedging mechanisms and insurance which tempered the peaks and troughs. Basically, if you can predict a pattern of movement, you can profit from it, and thus reduce the movement. You can see this with the "btc always falls in price over the weekend" that was occurring in regular intervals earlier this summer. If it can be predicted, people buy and sell in anticipation of profiting from such foresight and ultimately diminish the move they were predicting.
Bitcoin will be volatile for a very long time, but ultimately it will (like all goods and services) tend toward efficiency and stability.