Q: Any ideas why these branches died?
A: I don’t know why ‘Sky Pencil’ holly does this but I have seen it before.
Clip the dead branches at a spot below the brown leaves. Use a knife to gently scrape away the bark. Look for tiny holes that indicate black twig borer.
If you find the tiny holes, there’s still not much to be done. Black twig borer is just an occasional pest. Prune out dead branches and destroy.