The computers would still stop working eventually; the universe as we know it also has a finite lifespan, and a machine will always require some amount of energy to function.
Well, there is a notion that there is a Darwinian evolution of the Cosmos (https://arxiv.org/pdf/gr-qc/0205119.pdf), and one might argue that we can't be sure about the future of the universe (especially adding the unknowns regarding multiverse and that whole line of thought) and what future technology might bring, regarding even, let's be optimistic, potential changes to the fabric of timespace itself. Given the non-zero chance of a technological singularity happening even in our lifespan.
