I believe that state is Starforce, as it's the only one not removed on KO; using the Phoenix Phormula reveals that you've got 13 Starforce after being KO'd.
On that note, the passive states added by items (like the Haunted Aegis) really should remain after getting KO'd as well- I'll get around to making that the case tomorrow, along with probably setting the transfer event so that resetting doesn't put you in front of that enemy.
(EDIT TOMORROW: Shoot, was busier today than I'd expected. Well, it should be possible on Sunday!)