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?
I hate to sound like a fatalist ... but my question would be 'why would anyone want to live forever?' It just seems to me that there would come a time when you've done everything you wanted to do, seen everything you wanted to see, and would be faced with an endless, boring existence.
This also adds an element of selfishness. Why shouldn't new people be born to replace me and have the experience of life? Clearly you couldn't still reproduce and have this world as you outline it. It's seems more problematical to me than it would be of value. Maybe that's me though.