I don't see an end of the world as strictly necessary. Rather, the world reaches higher levels of entropy/complexity over time, which makes any worldview made within it decreasingly able to predict with high precision over time, necessitating the creation of new theories. I see no more reason to think the universe started alive and is ever dying than to think the universe started dead and will become only ever more alive over time. Though this doesn't mean humans in particular will continue, I think we have a reasonably good chance of making it to interstellar travel.
In terms of more general far future timelines, if Jeremy England's theory of life's relationship to entropy (which is that matter takes on life-like properties as part of increasing entropy) is correct, we should see the world become more alive as entropy increases. Given that entropy is limited by the Bekenstein bound, which is proportional to space as well as energy, and that space seems to be expanding, there's no reason to expect entropy to reach a limit. So I think life will, if given enough time, simply take on forms that our current understanding is insufficient for predicting, rather than dying out.