Interstellar Distances are just too large and they can't use high atomic number elements
I'm going to assume you want them to be able to venture into space at least to their other habitats but not much further than that.
Right now they may have access to asteroid mining where water is abundant. That gives them access to create hydrogen and oxygen propellant, which is what's used in modern chemical rockets. Hydrogen and Oxygen have smaller atomic numbers, so they're much easier to find out in space. Anything with a higher atomic number than iron needs to be created from a supernova. If they live in a region of space that has a lot of small stars, there aren't going to be many supernovae, so there's going to be very little of any high-density elements. Any high atomic number element like Gold could be used as the fuel, which is rare in space.
If they live around an average star, the nearest star to them is going to be 3-10 light years away. If we take the fastest speed any spacecraft built by people and assume that their spacecraft can exit their system with this much speed (which probably isn't true), it would take them 4060 years to reach a star the distance to Proxima Centauri, the nearest star to Earth. It's just not viable to send a rocket to another system because of the wait calculation. 99
The wait calculation is question of whether we should send a craft to space now or wait later. If we send the spacecraft too soon, a new technology will reach before that spacecraft gets there. If we send it too late, we lose time to be at our destination planet.
It seems like your civilization has endured some losses in many respects including their home planet, why not technology? They may have some experienced people but not enough to create an interstellar drive. Consider what <PERSON> said,
"You are obviously able to use a computer, like billions of people worldwide. And there are many millions who can program a simple website. But how many can design a microchip, or manufacture one?"
Gaining the technology to achieve interstellar travel from local travel is like technology jump from going to a bronze sword to an AK-47 or from an AK-47 to a guided missile. What makes this even harder is that advanced technology almost always requires access to new and unique materials. Why should an interstellar drive be any different? Just make stringent technology requirements on high atomic element materials, and your civilization will have a hard time acquiring it.
None of these obstacles make interstellar travel impossible, but it should take your civilization a couple hundred years (very rough estimate) to develop interstellar travel at the soonest. 199