It's just wrong. The immune system eventually wears out, if you live that long. By the time you are 112, you may be down to one or 2 clone lineages of B and T cells. So you won't mount a great response. But, the design of living organisms is that they are self-renewing colonies of trillions of cells that work together. The immune system can keep fielding new challenges just fine. In fact, allergies are an instance of immune systems not having enough to work on. So, kind of like a bored kid, those cells find SOMETHING to do. (Like the time when I, at the age of 7 got a saw for Christmas from my father. It was supposed to saw through steel and wood, anything. Bored me, I tried it out on my dad's rolltop desk... :-D It's funny now. It wasn't then. Anyway, an immune system without enough to do is something like that.)

There are people that inject snake venoms to the point that they are hyper-immune and can take a mortal dose of venom without serious harm. It still hurts terribly, but they recover in a day or so. The only indications I have on those people is that they have better health for longer lives.