Bitcoin will continue to exist as long as there are computers connecting to each other over the internet. Simple as it sounds.
While that is true if bitcoin was only used by two people that exchanged bitcoin among them, bitcoin will still technically exists and be used but at that point bitcoin will be useless and irrelevant and I think that is not something that anyone in the forum wants, so it is not only a matter of survival it is a matter of bitcoin being useful for the people and I do not see a reason why bitcoin will stop doing exactly that especially now that segwit has been activated.