It is hard to predict with certainty, but usually if something is going to fail it is during its early years. Since Bitcoin is approaching 10 years it is probably past that hurdle. I would think it will probably be around for the next 10-20 years easily, then it may risk being supplanted by some other coin or even technology. It probably won't go away completely, just become not as relevant at some point.
That's true, it's hard to predict with certainty, because for one, bitcoin or cryptocurrency, for that matter, is not certain in itself. Therefore, to just answer the question plainly in terms of how long will it survive won't be an easy question to answer. However, I think it has a real big potential to survive and be there for a long time, especially with the improvement in price value it has shown to do in last few months, plus the growing attention that most people have for it right now. I think if all good factors come into play in its favor, then it is certain that it would be blessed with longevity.