I actually think that it will stabilize when the number of people using it stabilizes for a long time. Perhaps that will happen after some bubble bursts.
And perhaps it will never happen. Given that the number of computer and internet users hasn't "stabilized" until now and is not expected to stabilize in the foreseeable future, what makes think the number of bitcoin users will stabilize anytime soon, if ever? And even if it stabilizes, we still have the 19% deflation problem!
I don't see the 19% deflation as a problem.