Global warming, nuclear winter, asteroid hit, massive solar flare, supervolcano, plate tectonics - anything we care to imagine will leave the Earth much closer to being habitable than Mars.
Just playing along...
But how do you know this? Are there any papers or reports that say that a thousand years is the lower bound on a self sustaining colony on another planet?
It seems to me that this idea is a common wisdom that people often say because in their mind colonization is an out of reach idea so they just pick a random big sounding number like "a thousand years" as a placeholder for 'it is impossible" when there isn't any actual research that says it will take a thousand years.
Think about how economically unviable and hard it is to just create 1 new chip fab on Earth. And think about the fact that on Mars you would need to re-create the entire supply chain that already exists on Earth. Remember that the minerals that you need are probably about as spread-out on Mars as they are on Earth, so you will need a global network of mining stations and processing plants to get the various necessary metals - all this without any access to fossil fuels of any kind, and with all of humanity spending little time outside for fear of radiation.
Perhaps establishing a colony that gets the vast majority of its supplies from Earth is doable in a generation or two (though of questionable value). But creating a self-sustaining colony is entirely out of reach for the forseeable future. You don't need actual research to tell you this any more than you need actual research to tell you that humans can't flap their wings to fly - a little bit of back-of-the-napkin calculations will quickly elucidate it.
The sheer population needed to run a complete supply chain for high-technology (on which Mars would be entirely dependent for basic life-support) is staggering. Having the entire thing built and operated underground would be an engineering and social feat of unprecedented scale in humanity's history.
Iamgining doing it in a generation is simply impossible. Its more likely to happen by quantum fluctuation in a second than by humanity's efforts in a generation with current technology.