I think it will survive until people believes in the technology. Since bitcoins can last indefinitely in theory, bitcoins will be relevant if there are people that are willing to buy and sell it. The 21,000,000 bitcoin cap is just the number of bitcoins that will go out in circulation. The part of mined block, is just actually rewards. Miners can still continue mining blocks even without rewards. I guess that's a good thing for us, since our transactions will still be written in the blockchain. But I don't think I'll live to see that day since it's so far away.
In my opinion, I think bitcoin will last as long as there are people keep on using it in transactions, payments, investments and so on and so forth and keep on interacting or navigating it. It will also survive as long as there is an internet connection for us to be able to post,read, answers and join in this forum. Bitcoin will not die if all of us or even most of us will trully support it and introduce it to others and ofcourse it will remain for so long and will not end if only we accept it. So I guess, bitcoin can survive for years or even century if we do all these things.