It takes a lot of parts that come from different sources and also sensitivity to place every screw correctly. It might be very difficult for a purely robot-run society to reproduce the robots themselves successfully.
You might have a factory that creates trucks, but who creates the robots that work in the factory? They’re a different type of robot, and if you have a factory to produce them too, who produces the robots that work at that factory? The issue might be very difficult, and even if it’s possible, you probably would need a very large industrial system to successfully and reliable reproduce every type of robot.
Meanwhile (biological) living beings can reproduce themselves successfully, especially plants, given nothing but water, CO2, some sunlight and some mineralic fertilizer (which might already be present in the landscape). That ability to self-reproduce is amazing and might be what makes life special.
These thoughts are relevant because it might mean that robots can never really get rid of humanity, i.e. overthrow humanity’s rule and kill all humans. At least a few will be needed forever to ensure the robots can be reproduced. So you have something like: Humans reproduce themselves and also produce machines, which then do most of the hard work in the world. Kinda like DNA produces proteins, which then does most of the biochemical work inside a cell.
Bootstraping is what you are looking for. A lathe is often the start of bootstraping because a lathe can make itself. You can also use a lathe to make a lathe, but if you do it that way you slowly lose accuracy over generations (but it is much faster and so most lathes are made with lathes). By having a lathe make itself you restore accuracy (and if you have learned something can sometimes get even higher accuracy than previous rounds). Before you can make a lathe you need precision flat surfaces, but it turns out only basic tools are needed to bootstrap that (and a lot of time). A lathe is considered a machine.
The point is that robots can make themselves if you program them for that. I’m making a clear distinction between reproduce themselves and make themselves here. A nearly worn out robot can restart the whole thing (so long as it does fail completely too soon) of making a new robot that is bigger and more accurate than it ever was (if bigger and more accurate is desired by the programming). That doesn’t mean the same robot could reproduce itself, instead it has to cause a robot to make itself.