To answer you question based on the information given, it sounds like it's not eating them because they are rubbish, and because it's not particularly hungry, so it doesn't think it's worthwhile to tackle them.
What should you feed it? The leftovers (I'm assuming this is flakes falling to the bottom of the tank) are fine, and you could suppliment with bloodworm every few days as they really seem to enjoy this.
Another thing I'd add is that you should get more corys of the same species, corydoras are naturally gregarious, keeping one on it's own usually effects the behaviour of the fish and could possibly have a long-term effect on health. Regardless of how long you've had your corydoras or how healthy it seems, if you have the space you should try get it some friends of the same species.
If you don't have space...can you describe it's usual behaviour? You might be OK, and corys often are on their own, but I've seen them do badly too.