Which cosmologies support Eternal Life? Which cosmologies consistent with physics as we currently know it is consistent with Eternal Life lasting forever starting from here on Earth while preserving the memories of human life? With computers and robots colonizing the universe and growing without bound?
Tipler had suggested an Omega Point associated with a big crunch in a closed universe, but unfortunately, scales below the Planck length do not exist.
Dyson had performed an analysis in the article "TIME WITHOUT END: PHYSICS AND BIOLOGY IN AN OPEN UNIVERSE".
 A: Dyson's models do not work because we live in a phase with a positive cosmological constant. This leads to a de Sitter horizon which limits the possible growth of computational capacity, and the best we can hope for is Poincare recurrence assuming causal horizon complementarity. Besides, if superstring theory were true, our nonsupersymmetric phase can only be at best metastable. Its lifetime might be exponentially long, but that's still finite.
Leonard Susskind and Shenker are working on the Census Taker's Hat, which might be just what you are asking for. In the landscape of string theory, there exists supersymmetric vacua with exactly zero cosmological constant. It's possible for our phase to tunnel to such a vacuum in the future. The future conformal boundary of the new phase will be a null "hat". A Census Taker with eternal life will enter the new phase and grow without limit and finally end up at the Census Bureau at future conformal infinity. During its lifetime in the new phase, the Census Taker will emit massless radiation heading off to the Census Taker's Hat (i.e. future null infinity). This will continually transmit information from the Census Taker to the Hat where they will be recorded holographically. In this article by Leonard Susskind and Raphael Bousso, they claim that

Over time, the Census Taker receives an unbounded amount of information, larger
  than the entropy bound on any of the finite causal diamonds beyond the hat. This
  means that the Census Taker will receive information about each patch history over
  and over again, redundantly.

and this will happen infinitely many times.
Unfortunately, information represented holographically at the Hat will be frozen, and to give them eternal life, there needs to be someone outside our universe to read and interpret them. This can happen if our universe is really a computer program running a limit computable simulation. After some finite time, this simulation will be stopped and its output processed. This corresponds to an ordinal jump. To have eternal life, we need infinitely many ordinal jumps all the way to the ordinal of all ordinals, which is itself not an ordinary ordinal. We have to push past the uncountable $\aleph_1$, but this is fine because of the Lowenheim-Skolem theorem ensuring the existence of nonstandard countable models. A limited weakened form of the axiom of countable choice is guaranteed by the probabilistic interpretation of quantum mechanics.
A: As the OP had already mentioned, Tipler's Omega point cannot work because nothing smaller than the Planck scale can exist in quantum gravity. Dyson's proposal of intelligent beings hibernating for longer and longer periods between thoughts just might work if the cosmological constant is zero, as commonly thought when Dyson came up with the idea, but not with a positive cosmological constant. Sad to say, hibernating is not enough in an accelerating universe because the parts making up the intelligent being will be ripped apart until all that is left is a thermal state at the de Sitter temperature. The smallness of the cosmological constant means that the de Sitter temperature is so low that it will be practically a nearly perfect vacuum. Creating a bubble universe in a laboratory will not work either, as spelled out by Guth and Farhi. The bubble universe will collapse into a big crunch under some fairly generic assumptions.
Our civilization is doomed to oblivion. All our joys and sorrows, the good and the bad, all our struggles and achievements will come to nothing. All that we cherish and hold so dear will not last. All our efforts at technological advance and development are futile and will end in ruin. All our quest to learn about the universe in the form of science, to solve the mysteries of nature and keep expanding our knowledge are ultimately pointless in the grand scheme of things because our knowledge will not last.
A: The best theories of cosmology today predict a big rip. The universe will keep on accelerating with a positive cosmological constant until everything is diluted away into a vacuum. Unless a catastrophic decay into a more stable vacuum happens before then.
But there is a way out! Fear not! What if our universe is some computer simulation in some higher plane, let's call it "heaven"? Then, before the big rip destroys all life in the simulation, some "god", i.e. computer operator in "heaven" saves the informational patterns of some lifeforms and "resurrects" them in heaven? Saved by deus ex machina! Have faith and believe, oh ye of little faith. Have faith in deus ex machina as your personal savior.
But heaven might not last either... Heaven and earth will fade, but the LOGOS, the informational patterns will still remain in a new heaven and a new earth. Visions of a new heaven and a new earth...
A: The laws of physics are not fixed in stone. The laws of physics are still evolving and in the process of formation. There is a superposition of the laws of physics which gradually gets more refined as we learn more and more about our universe. The highly respected cosmologist Paul Davies explains this well. There are many laws of physics compatible with what we already know from experiments. Some of them support eternal life while others don't. Those which don't get culled. This is a completely naturalistic process. The universe is creative and continually finds new ways to live forever.
