If I am immortal, I am bound to kill myself some time or another. We are animals, we are instinctively wired to breed and then die. Sure, human instincts are more sophisticated, we have a hunger for knowledge, entertainment etc., but the will to pursue these endeavours wanes with immortality. After a thousand years, I will have been in every country on earth, used every drug, followed every dogma, raised many children, and studied many books. Sure, developments like space travel might bring in new elements for enjoyment, but will you still enjoy it after 10 000 years? 100 000 years? Things will get repititive, dull, meaningless.
After that period of time, a bullet to the brain will be salvation.
We only enjoy life because life is finite. We only seek success, happines and companionship becuase life is finite. We only invent reasons to live because life is finite. What then shall we do if life is infinite?