From memory it respawns the low level enemies constantly, since they're just ammo/health/armour pinatas. You needed to kill the big enemies to complete an arena.
Not really a fan of the design choice, but I had a decent amount of fun when I clicked with how the Devs wanted you to play.
I convinced my partner to play it recently and the way I knew she'd finished it was that I could hear sniffling from the desk behind me.