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qmotus comments on [spoilers] EY's “A Girl Corrupted...?!” new story is an allegorical study of quantum immortality? - Less Wrong Discussion
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If there is any sequence of events with nonzero probability (more precisely: whose probability of happening in a given period of time never falls below some fixed positive value) that causes the irrecoverable loss of a given mind-state, then with probability 1 any given mind-state will not persist literally for ever.
(It might reappear, Boltzmann-brain-style, by sheer good luck. In some random place and at some random time. It will usually then rapidly die because it's been instantiated in some situation where none of what's required to keep it around is present. In a large enough universe this will happen extremely often -- though equally often what will reappear is a mind-state similar to, but subtly different from, the original; there is nothing to make this process prefer mind-states that have actually existed before. I would not consider this to be "living for ever".)
Maybe not. But let's suppose there was no "real world" at all, only a huge number of Boltzmann brains, some of which, from a subjective point of view, look like continuations of each other. If for every brain state there is a new spontaneously appearing and disappearing brain somewhere that feels like the "next state", wouldn't this give a subjective feeling of immortality, and wouldn't it be impossible for us to tell the difference between this situation and the "real world"?
In fact, I think our current theories of physics suggest this to be the case, but since it leads to the Boltzmann brain paradox, maybe it actually demonstrates a major flaw instead. I suppose similar problems apply to some other hypothetical situations, like nested simulations.