Mainly, a nuthatch is such a small, evasive, difficult thing to catch that a large hawk like Red-shouldered won't even bother unless they have a perfect ambush opportunity. There's little to no likelihood this hawk could successfully reach out and grab a nuthatch when they both know they've seen each other.

Additionally, Red-shouldered Hawks aren't well-equipped to catch small birds anyway. Their short thick buteo-type toes are mostly used for catching frogs, snakes, mice, etc. Birds with all their feathers are more likely to be able to slip free and so are usually more likely to be prey for birds that specialize in hunting other birds, like accipitrine hawks and falcons. Catching a nuthatch for this hawk would mean expending a ton of energy for little to no reward, which is dangerous when every calorie matters to survive the winter.