Everyone loves to paint an apocalyptic picture of the future, but I'm willing to bet that decades from now, even centuries, society will be just fine.
The truth is this will happen more slowly than people realize. We are an incredibly adaptable society. The sticking points will become obvious over time and whole regions will learn to adapt. How do I know? It's already been happening for the last several hundred (even thousands) of years. So much of our society is already mechanized.
Imagine this exact debate in 1600s going on and someone saying, "what will people in the 2000s do if everything is mechanized?" Well, for one thing there are people working in industries using skills that were unheard of hundreds of years ago.
The argument about the accelerating rate of advancement is true, but only within very narrow sectors. You can't use that to describe all facets of life. Self-checkout grocery machines have been around for more than two decades and still we have cashiers. Vending machines were suppose to replace restaurants. ATMs were suppose to make banks irrelevant by now. Yet, these still exist. Not that they won't one day go away... it will just happen more slowly than people realize. It's always been this way and society adapts every time.