I feel that when someone says "As I said," , they are not just pointing out they are repeating something they said before. They are saying you are not getting what they are saying. Is this true? What are the common moods and thoughts one experienced when saying this?
As we say so often on this site, it depends on context.
Sometimes a person will say "as I said" just to remind others what he said before. But yes, if you need to re-state what you already said, often this means that the other person didn't understand you. (Which, of course, might be their fault for being dumb, or might be your fault for not speaking clearly, or might be nobody's fault and just a confusing situtation.) People often say "as I said" in an argument or debate to mean that the other person is deliberately ignoring your point.