The Thing and Petrina probably don’t quite qualify as hard SF, but they’re pretty close.
But one of the biggest problems I’m finding with trying to write hard SF is finding a reason to have humans in space at all. The SF traditions of Mars colonies and space mining really don’t work; there’s no reason whatsoever to mine things in deep space and ship them to Earth because the cost of doing so is far greater than the value. I’m sure we’ve all seen the ‘one single asteroid contains trillions of dollars worth of materials!’ articles, but even if you could find a cheap way of bringing them back to Earth you’re just left with a big rock in space to mine when you could be mining big rocks on Earth instead. Worse than that, while there may be billions of dollars of gold in that rock, even if you could extract it for a reasonable cost you’d just crash the gold market when you brought it back.
So no-one is going to be shipping iron ore millions of miles to Earth unless we have a sudden attack of nuclear-transmuting iron-eating bacteria which destroy all the iron, or some such insanely unlikely event. Any kind of cargo to be shipped around the solar system must be high value relative to its mass and difficult to make locally; complex electronics, perhaps, or uranium and other fuels with a high energy density. But by its very nature, that also means a limited market; an asteroid uranium mine, even if you could find uranium with a density high enough to be worth mining, would probably only be shipping out a few thousand tons a year which wouldn’t keep many freighters in business.
Habitats may be another option; people want somewhere nice to live, so if you can build them an O’Neill-style habitat then they would want to buy it. But then you’re back to a chicken and egg situation: before you can build habitats you need enough people to want them and those people need to be doing something that will pay for them to build those habitats.
Spacecraft construction is in a similar bind: we could build shipyards in orbit around the Moon or at L5 or whatever, but if there’s nothing for people to do in space then why would they buy them?
Telecommuting would be an option if you can do something that doesn’t require a physical presence. But telecommuting from light minutes to light hours away is always going to be less efficient than simply finding someone on Earth to do the job, and the cost of living in space is likely to make wages unaffordable compared to workers on Earth.
Developing dangerous technologies is another possibility; if you’re going to try to build self-replicating nanotech or genetically-engineered microbes, then being millions of miles away from anyone would be a useful safety feature. However, a society so scared of such work that it wouldn’t be allowed on Earth is unlikely to be willing to let you sell the products on Earth either; otherwise building a secure lab on Earth is likely to be much cheaper than doing it in space for the forseeable future.
Ultimately I can only really see two reasons, which are somewhat linked: ‘because it’s there’ and ‘because Earth is too dangerous’. Even if nothing else was to change then eventually travel into space will become cheap enough with increased productivity and improved technology that people will move out into space just because they can; but that’s probably at least a century away. This makes the latter seem like the only realistic justification for stories with significant numbers of humans living in space in the near term; technology which is capable of putting people there can also be used for massive destruction, so the only way to be relatively safe is to be as far as possible from people who might want to harm you. That would lead to a future of paranoid ‘city states’ in space where visitors were unwelcome and trade was minimised. Even then a redirected asteroid could result in a very bad day for your habitat.
Fear as the driving force also leads to some other interesting implications. If you want to be as far as possible from dangerous people then you’ll soon find that the Oort cloud is the place to be; it’s a long way from Earth, there are resources to exploit, and it’s so big that people aren’t going to find you easily if you choose to hide out there. But once you’re there and living in a self-contained habitat which isn’t reliant on the resources of the inner solar system, then why not just ‘push off’ into interstellar space? Even if reaching another star system takes a few centuries, you won’t really care as your life won’t really change. The big risk would be a major system failure in deep space that you can’t fix, but that wouldn’t be much different to such a failure in the Oort cloud.