It will  still be popular even if Bitcoin had a stable price. Most companies and retailers don't accept bitcoins  today due to its price instability. They all would start accepting bitcoin as payment if its price would  be stable.So, there will be a huge increase in demand for bitcoins which would increase its price and help  the progress of bitcoin , but since bitcoin is a decentralized currency, its price changes way to often  based on the increase and decrease of demand .