Being immortal doesnt mean you're invulnerable too. You still may be susceptible to pain, illness, injury, and dismemberment. Would you like to spend the rest of eternity crippled? Missing limbs? How about ravaged with disease? Would you age? (If so, would you wither away to dust? (sentient dust?))

Theres more to immortality than just living forever. If anything, it's more of a curse than a blessing...

If you have time, you may want to take a look at Tuck Everlasting by Natalie Babbitt. A young girl is faced with the gift of immortality, and the perils that may accompany it.