Correct me if I'm wrong, but I think that the definition of "immortality" has been (for the last couple pages of this thread at least) true, hard immortality, where you do not die, ever, for any reason, and you live for infinity, regardless of the fate of our universe.
i believe it is our destiny to transcend time and space, thus achieving this kind of immortality by kind of existing "above" this universe and all of its time.
Infinity is infinity, so even achieving immortality in this way may not guarantee reprieve from a death outside this universe. In other words, maybe you can be "infinity-style-immortal" with respect to THIS universe, but still be finite with respect to the multiverse.