I think Mei just prioritized her career over romance in her early life, and then was too busy with the revolution and restructuring Kiri into a decent village. Now that's she's finally ready to settle down all the good men are too awed/intimidated by her power, position and aggressive personality to approach her and she's bizarrely too much of a gender traditionalist (in regards to romance) to be the one to initiate things with a man. She literally dreams for a prince charming type to come sweep her off her feet, if a guy doesn't have the guts to ask her out directly she probably wouldn't even notice his feelings.
So yeah, her men problems strike me as being entirely of her own creation. Her standards are too high and kind of inconsistent. She's a powerful, independant woman who desires a very traditional romance, and that's unlikely to happen for a woman with her elite social class and political power. She probably has dozens of admirers in Kiri but she'll have to approach them if she wants a relationship.