The way we think about time is very human-centric, and specifically it relates to individuals, not even to the lengths of civilizations. Even a human civilization is expected to last at least a thousand years. As for 4000 years or even 100,000 years, that would be nothing much to an AI. It would purportedly take several hundreds of thousands of years before sufficient memory corruption sank in to the point where algorithmically repairing the corruption, even if in a low steady dose, would be akin to neutering the individual identity of the AI.