Inspired by this question regarding how Skynet preserved itself during Judgement Day.
It's easy to imagine that Skynet could preserve itself, especially considering it's a military AI that likely has unrestricted access to self-sufficient military datacenters. But, I'd imagine a full global thermonuclear war would destroy mining, refining, and manufacture facilities required to build a something simple as a flashlight, much less an advanced piece of tech like a Terminator.
Any robots that already existed within Skynet's network on Judgement Day would have to be physically altered to shut them down such as they could withstand EMP from the blasts, which means they could not be re-activated remotely. As mentioned in a comment, Reese told Sarah that some humans were kept alive to work, but there'd still have to be a mechanical presence to force the humans to work. Where did Skynet get its initial work force to establish its industrial infrastructure?