By the time children today are old enough to die from natural causes, we'll have a cure for that.
At some point I think we will 'cure' cellular senescence. Then humans can stay physically in their prime, indefinitely. But there are other limits, like memory. Because memories require physical space, there is only room for a limited amount.
I think we can get past that either naturally, by overwriting old memories, or artificially, by augmenting memory with technology. Research is already looking at brain augmentation with electronics.
So what will be the ultimate limit? Or will humans achieve immortality?
Well, we have to die, don't we? We make room for the next generation when we die or else we end up living "a la soylent green". What a mess that would be. Of course, I'm all for the cyborg idea that Scalzi develops in the incredible sci-fi novel "Old Man's War". Or even something like Haldeman's "Forever War" where people travel time-space during obligatory military duty. Immortality? Maybe. I'd rather die and be allowed to come back again to a better existence.