@Dragen
The main problem probably lies in her position, if she was mielle she'd have more control over her family and thus could have leveraged some control over her father, but since she's aria, he doesn't know where her alliagances lie and her father is probably on the side of the aristocrats, basically if she was mielle he could meet her with the argument that he knew her from the past and decided to say hi on isis's birthday, on the other hand as he is at a severe disadvantage at this point against the aristocrats and isis, so if word got out that the crown prince was meeting with aria and aria wasn't completely on his side, it could not only end badly for him, but could lead to the crown losing even more power.
TL;DR at the party he could have came up with a excuse saying "we keep meeting like this", but aria both has a repuation and isis is implied to outright hate her, he can't risk aria or even mielle (via aria mentioning it to mielle) letting isis know his plans or even that he's met aria like this, even unintentionally, as his ultimate goal is to weaken her powerbase.