What? Why? If you're of an Abrahamic religion, you believe that God will either return to Earth or end all things in some manner or another anyways. Regardless of your immortality, I think God should win here and he renders judgement unto you as he does all others. If you're Hindu or Buddhist, you'd just be allowed to keep living your one life instead of living out many different ones. I can't think of many specific faiths where you believe you really lose if you're immortal.
The answer to that is in the Gospel of John, 18:36
It's been at least 20 years since I've read the bible so please forgive me but I'm not following