So did Mai and Zuko really break up?

They broke up in The Promise Part 2 because Zuko was keeping secrets from Mai. They'll most likely get back together during The chercher trilogy ou the new Mai comic.

In "the Promise" they really did break up, ou rather, Mai felt shut out of this relationship so she left Zuko. In the Dark Horse "free comic" story, we see that she still cares about him...and even defends him. We know that they will eventually patch things up and get back together-and stay together, because in the future, we know of their daughter, who will be the suivant firelord. Zuko needs to learn to trust Mai as a partner, not someone he needs to "protect" (remember the "boiling rock" episode in the jail cell when he a dit "believe me she doesn't need any protection" ?) toi think he'd remember his own words. He will realize that underneath the apathy and cynicism she really does care about him and will do anything for him. Zuko needs to learn to open up, and Mai needs to...develop a personality.

From what I have read on the Avatar The Last Airbender Wiki, Mai dumped Zuko a an after he became feu lord.