The real question is, what do you define as its "life"? Would it still be the same atom if one piece were tossed to the winds?

If one change in the atom redefines it entirely, then yes, obviously, an atom (or anything else) is the same until it is unidentifiable to itself.

If you're asking if the unity of the nuclear bonds is forever, I'm afraid that it, too, is subject to the eternally shifting forces of fusion and fission. It doesn't quite "go" anywhere as a unit, it just rejoins the universal flow of matter of energy.

But then, that's the kind of things physicists say at funerals all the time.