Being out of memory seems unlikely to me. The sprite that is loading is instantiated quite a few times and I see newer versions of this just fine whereas the black boxed textures are pooled on app launch for the most part; there is a couple non-pooled sprites that are still drawn black. This problem existed before I pooled these sprite objects so I don't think that's the root of it either. So the Instantiated objects, which would be grabbing more and more memory, are mostly fine.
One thing I noticed in the inspector that is unique to the sprite that is working just fine, there is no material in its inspector view. The mesh filter lists the material for the atlas, but the material isn't in the inspector. On the sprites that are broken, the mesh filter lists the material and the material itself is in the inspector free for me to modify.