Aya in particular has the best AI survivability due to her high unfocused speed.
So she was probably at least 20 seconds away from going down.
Yep, more than likely the case. It's always hard to look at the enemy having only half a sliver of health left and assuming that it will be over soon. Most of the time, the AI will just refuse to die while you scramble to gather Spell after Spell in a hopeless attempt to bring the battle to a quick end.
Take it easy and enjoy, Stage 7 is almost always the coolest in PoFV. I think the worst I had was a 2 minute match with Aya in round 3, not like I mind battling her for more than 6 minutes total, Aya's moves and the BGM make it a lot of fun.
I think only Stage 9 is better as long as you're not getting curbstomped and can actually put on a fight, then it gets epic max, especially thanks to the BGM and the huge, huge amounts of bullets, not to mention the pressure. God, I love PoFV.