Yes, they must, if only because the conditions that make life possible are not themselves eternal. The number might be far larger than today’s practical limit, but there will always be a number, whether we know it or not.
Besides, who wants to live forever? Always worrying about one’s income or investments, always dreaming of the days when the pretty girls didn’t sneer and walk away, always straining to come up with new and inventive ways to yell “Get off my lawn!” — ? Blech.
Even if immortality somehow encompassed being insulated from the worries described by Francis and Dick above, there is one malady that neither technology nor magic can prevent: boredom.
In my darker moments I suspect that sooner or later God’s going to remember this universe He created and played with for a while, and wonder why it’s still gathering dust on that back shelf when He could use its components for something more interesting.