Yeah, "unique", in the context of this game, usually means an idol that only shows up once .
All idols have sexual preferences, and romantic success also depends of your friendship level with the idol. If she's constantly rejecting you, it's either because your friendship level with her isn't high enough, or because her sexual orientation does not include your gender. Keep in mind that rejection can also happen if the idol has the Asexual trait, or if she's already in a relationship.