It will become more popular, because larger organizations will consider to use Bitcoin to transfer payments and won't need to worry about daily price fluctuations.
It can of course, at a constant interest in Bitcoin price remains at large organizations. But people have lost interest in this.
Exactly they would switch to other coin which has more volatile price and traders would like that and its not only a small portion because big investors do also like on bitcoin because of moving prices and if bitcoin would stable its price then popularity would somehow decrease.