When you start talking about timescales like this, you have to shift the way you think entirely. The meaning of "surviving" starts to become tricky. You're operating on timescales where evolution of species starts to become a meaningful issue. Indeed, it forces us to recognize that "species" isn't even a natural concept. It's a man made one used for categorization. The genomes in question flow fluidly from one generation to the next. DNA from bacteria finds its way into human genomes. Nature doesn't care about our boundaries.
The same issue arises with societies. Was there really a transition from Confucian China to Daoist China? Or was it just a fluid series of events which we call a transition in retrospect? Should we say the Confucian society "died," and a new Daoist society was "born," or should we say that the Chinese society "evolved?"
Is the Voyager probe an "escape?" Or do we need a person on board for it to be an escape? What about just a vial of H. sapiens DNA?
To deal with these questions, I find it is most meaningful to look at individuals as a reflection of the universe around them. They're a fixed point, mirroring the world and themselves within the world. This is why "escape" is such a big deal. If just one reflection of a society gets free, that society can be mirrored once again upon whatever grounds the escapee lands in.
Have you ever pointed a video camera at a monitor displaying its own feed? The pattern dances around, but often there are single points on the screen which remain constant, black or white, because the camera is looking at the exact same pixel that it is outputting. Those are the fixed points in question. And, being reality, they're imperfect. One lone survivor of Nazi Germany may not be able to carry a perfect enough image of the Third Reich to rebirth it. That society may indeed die with its last individual. The image may simply lack the fidelity to resonate in the new landscape, and die out like so much thermal noise.
So when you start asking about how advanced a society can be and still be trapped like this, its a curious one to explore. You don't actually have to trap all of the individuals, you just have to trap the ones who mirror society with sufficient fidelity. Consider a society where religion and technology are entertwined. The technology fuels the success of the religion, and the religion passes down the skills and knowledge needed to manage the technology. Let's say this religion has a rule that you never leave your planet. It happens. The only potential "escapees" are those who are insufficiently indoctrinated in the religion to have this mindset. But then they also lack the knowledge to reproduce the technology. An escapee cannot bring their society with them.
You could also have a species that has made a fatal mistake and all they are doing is stalling for time. We see this in the Asgard of Stargate SG-1. They accidentally made all of their species sterile. They live a long time, but as they die, their society dies with them. They are an ironic twist on your question. They are spacefaring, traveling the stars, and yet they cannot save their society. Their society spans planets, yet is dying.
The universe can also be terribly inhospitable. Consider the extremophiles of these societies, the ones which buck up against the limits of the heat death of the universe. You can have FTL, but it won't do you a lick of good once you exceed the half life of protons, and there are simply no planets outside of your protective technological spheres to colonize. This is explored in Stephen Baxter's book Manifold Time.
Or perhaps the mistake is in our definition of a dying planet. If we look at a planet, we may see death, when they see life. Consider a tree in winter. It's easy to say the tree is dead, but any gardener knows that there's still life there when you know where to look. The deserts of the Australian Outback are famously dead, but the aborigines native to the area know exactly where to look to find food and water when they need it.
Going back to Stargate SG-1, we also have the Nox. The Nox inhabit a planet which we felt was dying because the Gua'uld were coming, and no planet survives that. But the Nox were some of the most technologically advanced species in the galaxy, and they saw no threat from the Gua'uld. They felt their planet was more than lively enough.
So where does that leave us? Anywhere we want, really. You're really only limited by your imagination, and any artificial limits you may place such as species boundaries. in 1883, Nietzche wrote Thus Spoke Zarathustra, we find The Last Man, a society which spends all of its energy just continuing to be a society. It slowly decays, never once looking to the stars to escape. We've had over a hundred years since he wrote that, and so many technological revolutions that we don't even track them any more. Surely there's room for imagination more!