This is an open question, and one that will be decided in the branch of physics known as cosmology. Since time is best conceived as a dimension of the universe, and as we do not now know the long-term future of the universe, this cannot be answered at present.

Thinking of time as flowing obscures far more than it clarifies, on my view, and I think that the river analogy is dangerous. Anything that flows flows at some rate. How fast does time flow? Sixty minutes per hour? The image raises the prospect of a supertime against which the flow of time occurs, and that raises a nasty regress. Better to think of time as a dimension of the universe, but one that is anisotropic,t hat is, one in which going in one direction is different from going in another, unlike, say, East-West travel.