I've been fascinated listening to a podcast on the History of Rome (highly recommend). Rome wasn't built in a day, but also the fall of the empire was a period of about 300 years during which Rome itself was still called the "eternal city".

Not saying this as proof that the world is definitely going to shit, the point is that it I don't think we've achieved some new level of eternal civilisation that couldn't possibly fail. Every civilisation believed that right up until the point it stopped being true, so we should be on the look out for threats and not assume it will all end up OK.