To even consider "immortal" as possible suggests someone hasn't had a lot of formal math training. Infinity is rather large. In an infinite amount of time, any possible conjunction of circumstances that could cause an immortality system to fail will happen. Talking in thousands, millions or even billions of years doesn't even need to be rounded to be basically zero when compared to eternity.

Death is a certainty. No amount of technology can change that even theoretically. We don't even have reason to be confident that the universe itself is eternal, let alone any component of it.