Since you seem to want to have people attempt to comment as advocates for death, and generate possible counter arguments to provoke new angles of thought, I accept your challenge and will try to come up with a plausible sounding argument for death and a self contained counter argument that you can consider.

Beginning Death's advocate:

I'll start off with a quote from Hanson: http://www.overcomingbias.com/2011/10/limits-of-imagination.html

Our finite universe simply cannot continue our exponential growth rates for a million years. For trillions of years thereafter, possibilities will be known and fixed, and for each person rather limited.

The article goes into it's own details, but the general point is: Exponential growth eventually ends unless we simply have infinite space/resources. Hanson has several examples and he has run a variety of numbers.

So clearly, we simply have our immortal population producing new immortal babies at a constant rate, Unless we first gain such unlikely powers as generating new universes filled with such useful things as empty space and atoms out of thin air.

I'm willing to accept immortality as physically possible out to billions of years, but it seems stagnant. Let's call this "Immortal Steady Population." And I'm willing to accept a 1% of the population forming new babies for billions of years, without immortality. Let's call this "Death, with Babies."

But I'm not willing to accept BOTH as physically possible. We run into Hanson's exponential limits far before we reach billions of years. We can have, at best, "Immortal Steady Population" or "Death, but Babies." But we can't have "Immortals with Immortal Babies." at least, not for any substantial amount of time, without infinite resources.

Our very existence revolves around spreading our genes and making new babies. I can't accept not having that.

Therefore, to fulfill our life's purpose as baby makers, we must allow ourselves to die at some point. Without death, life has no purpose.

Ending Death's advocate.

Starting possible counter argument. I'll call it "The Fusion Argument":

Imagine if two immortals could fuse together in the future. You would take two unique individuals, and have them combine together into a single individual, who only needed one person's worth of resources, and was still immortal. You then combine their genetic material, and make a fresh immortal baby, without the accompanying memories. So I and a fusion partner could accept being only "half people" by fusing into one being to diminish our resource use, and as a single "parent entity" we can have a new baby. The overall population doesn't change, but no one individual actually dies. Instead, the "death" if it even makes sense to call it that anymore, is shared between the two people who want the new baby, who are forced to become one person to make up for what would otherwise be an untenable resource demand.

Also you could rearrange this further: 3 parents form 2 people and 1 new baby? That's fine as well. 3 parents form 1 existing person and 2 new babies? If that's what they want. Two people fuse into one, but have the baby also take genetic material from a third person who is not personally diminished? Needless to say, there are a lot of possible combinations here.

Ending possible counter argument.

So given the choices I mentioned:

1: "Immortals with Immortal Babies." (Impractical for long periods of time as per Hanson, without infinite resources)

2: "Immortal Steady Population" (No new Babies! Doesn't appeal to people who feel the need to make new life.)

3: "Death, but Babies" (A standard argument for the way things are, but doesn't allow for immortality.)

4: "The Fusion Argument" (A demonstration that there are other ways of handling things like death and new life.)

The Fusion Argument sounds like a pretty good. I gain all the benefits of immortality to begin with.

And if I want, I CAN have babies to make new life, and if I can find someone else to help and we can work out an appropriate division of our diminished cognitive/biological resources.

There might even be further possible states, although none immediately come to mind.

Do you find the argument and counter argument as presented interesting?