There is evidence that aging stops. True, for humans it does so only when we are already decrepit and stand a substantial chance per year of dying.

Interesting, if it's true the implications would HUGE, but then what mechanism would mediate aging and the eventual stop of it? It all seems rather counter intuitive - at lest to me and reading the preview made me no wiser:

First, aging is not a cumulative physiological process. Second, the fundamental theory that is required to explain, manipulate, and probe the phenomena of aging comes from evolutionary biology. Third, strong-inference experimental strategies for aging must be founded in evolutionary research, not cell or molecular biology. But there are also significant consequences of this work for human aging. First, biomedical strategies that are founded on the traditional cell-molecular theories of aging are bound to fail, because their fundamental premises are incorrect.

BTW here is a video about the long lived flies aka Methuselah Flies

Edit: I looked through the 55 thesis, and got a somewhat satisfactory answer.