The price of bitcoin will not always go up and will not stabilize at some price neither will it always come down.
One cause for the fluctuations in the price of bitcoin is it's volatility. The volatility of bitcoin, being one of the very nature of bitcoin, cannot be eliminated and will always be there. This is why there will always be pumps and dumps in the price of bitcoin.
I'd advise you to sell your bitcoins as soon as there is a profit for you cause no one can say for sure what will happen to the price of bitcoin in the future as there may be a dump or a pump. Sell in order to be on the safer side and not later regret.
Stability is not going to be a part of bitcoin as bitcoins price use to increases and it can decrease so it is all about our way of investment and our knowledge, if you will invest in bitcoin today and will hold your bitcoin for some time you will see bitcoin price higher than your investing price of bitcoin, so in short I want to say bitcoin use to move upward and downward but the travel of bitcoin downward come for very short time but most of time bitcoin remain at very high price it does not decrease very high but bitcoin use to increase very high.