If you think about it, every society above the hunter-gatherer level has been "unsustainable" in one way or another. It's by no means a new feature or one restricted to industrial society. Yet over the long haul, the positive feedback mechanism between population growth and technological advance has remained intact. One civilization may not be able to resolve its immediate problems and prevent its collapse, but another civilization comes along and revolutionizes those old techniques. It's at least true of the trajectory followed by Eurasian cultures since the late Pleistocene. Every solution gives rise to a new set of problems, and every new set of problems inspires a new set of solutions. The transitions are anything but smooth, and they're usually disadvantageous to individuals people and individual societies. But one can easily perceive a general advance in the aggregate.
Hell, even hunting and gathering societies haven't always been sustainable. The Clovis culture wreaked widespread ecological havoc on North American fauna, hunting many species of animal to extinction. One doesn't need an extraterrestrial cause to explain the end of the Clovis culture. They were the Native American equivalent of suburban sprawl today. Just spread out and use it up! The same thing happened in Australia when hunter-gatherers arrived there. They hunted many species to extinction. It was a completely unsustainable way of life.
I'll be even more provocative: life itself is "unsustainable". Environmentalists talk about how inefficient and wasteful modern society is. Newsflash: over 99% of species which have ever existed have gone extinct. It took just that much trial and error—probably 4 billion years worth of it—to create life that even had the concept of "sustainability". Anyone who thinks the universe or life were designed "intelligently" needs to stop and wonder why even an imbecile couldn't come up with a system less efficient, less "designed" than evolution. It's a mess.
This idea that everything on Earth is interconnected into a harmonious whole, and it's humans who have disrupted it, has begun to come under attack. Paleontologists now believe that life itself on several occasions has brought about widespread global catastrophe. We hear every day about the dangers of CO2 in the air (and rightfully so), but how many people know about the oxygenation catastrophe that overtook the entire globe 2.5 billion years ago? Cyanobacteria pumped oxygen, a poisonous gas, into the atmosphere, and it probably led to a global extinction event. I wonder if any wise, environmentally-minded bacteria said, "Hey guys, wait a second. I don't think this toxic waste dumping is sustainable!" Of course then we wouldn't be here to talk about it. Oxygen is poisonous to us, too, which is part of the reason we age and die. A perfectly unsustainable form of metabolism, if you think about it. Except we circumvent the catastrophe just long enough to have science, learning, love, and humor.
So there's never been anything remotely ecologically sustainable about human existence or even about life. The main threat to life has always come from life itself, not from bollide impacts. Yet life is robust. It only had to have happened once, such that every living thing today is descended from the same universal ancestor that existed almost 4 billion years ago. That means that the response of life to its inherent unsustainability is to surpass its own limitations. This produces new problems of sustainability, and yet life (and now intelligent beings) step up to those challenges, too.
I think the trajectory of this - at least now - is toward the problem of energy simpliciter. Not just the problem of food. Not just the problem of motive force. Not just the problem of fuel. But the problem of energy itself. If we do experience a technological singularity this century, then by the end of the century, non-biological intelligence will far outstrip biological intelligence in our civilization. Our problem won't be producing food, obviously. The main problem will be (a) how to perform computations using the least amount of energy possible and (b) how to keep the temperature of the process below that of a few thousand solar mass stars. We'll have to keep taking in energy from the universe (photons) and exploit cold spots.
But the universe is horribly inefficient. The energy produced per cubic centimeter per second in the center of the sun is approximately equal to the energy density produced in a compost pile or in a lizard's metabolism. It's owing to the sheer mass of the sun that it produces as much energy as it does and goes as long as it does. So your woodburning stove - a manmade object - is orders of magnitude more powerful than the sun. It's very interesting how far the order and complexity of human invention already outstrips nature. The idea that superintelligent, non-biological civilization will simply become the hunters and gatherers of energy in the universe is ridiculous. That advanced civilization will have to produce its own means of subsistence just as much as we produce ours now.
Of course the ultimate sustainability problem is represented in the laws of thermodynamics. This is the problem Asimov deals with in The Last Question. According to inflationary cosmology, the universe is the ultimate free lunch, essentially created out of nothing. A superintelligent civilization might be able to exploit this subtle fact of science in much the same way as engineers are able to exploit subtle differences in air pressure to generate heavier than air flight. My guess is that there are many degrees of creating something from nothing, and that the generation of the cosmos is the most inefficient way we'll discover. The power of intelligence might one day far outstrip the power of nature even to produce a universe or a multiverse.
In short, there might always be something like a "sustainability problem". But if the past is any indication of the future, such problems will not be the end of the story but just another beginning. Even if intelligence is not eternally capable of surpassing every natural barrier placed before it, it seems to be in its essence to try.