For example: I get a heart attack at 82, but one version of me doesn’t, and so continues living. Then, at the age of 85, another thing happens, but in one version, it doesn’t. How long can this go on?
Personally, I disfavour any model with infinities in it (infinite universe duration, infinite spatial extent, infinite branching of wavefunctions, the infinite ensemble of possible multiverses in The Mathematical Universe) because all of them suffer the same Bolzman-brain cognitive instability.
But the thing I don't understand about all this is that if the many-worlds interpretation accepts quantum immortality then wouldn't that collide with the second law of thermodynamics?
That is, under quantum immortality, your body will keep accumulating non-lethal damage and your suffering will never end. It's quantum immortality, not quantum eternal youth.
With that, probably until we die of age, so, 120-something?
But this is too speculative and with out understanding of world - impossible