The black sealer is a liquid asphalt sealer. Nothing will stick to for very long. You could simply get more sealer and reapply a fresh coat. Most likely the "chunked out" areas was caused by ice, freezing water, that got in or under the sealer. These areas can be patched with a concrete patching compound before resealing.
I would get some more asphalt sealer. This is cheaper and faster. Also you should dig around the foundation to seal below the soil line as best as you can.