... there you are...

[Catbat]

Hi everybody!
Catwoman gave Batman a vicious beating during their first confrontation, but toward the end of the fight she seemed to change her mind and suddenly began to seduce him.

The scene when she runs her clawed hand down Batman's torso is very ambiguous, but, judging from his reaction, it's clear that there's something sexual going on... More precisely, we don't actually see how Catwoman used her hand on the batsuit so... let's try to guess! 

[The Dark Knight]

It's because she was seemingly in a weak position. She had been rescued and appeared grateful, lowering her voice and having a pleasant conversation. So I'd say the voice was the biggest seducer here. The hand movements just sealed the deal.

[Catbat]

So I'd say the voice was the biggest seducer here. The hand movements just sealed the deal.

Sound post, I agree with you.
I believe Catwoman wanted Batman to feel secure, so first she thanked him with seductive words that hinted at a possible truce between them (the unspoken invitation is that, since Batman saved her, Catwoman could reward him by giving him some access to her body).
So if her speech was meant to gain Batman's trust, Catwoman massaged the batsuit to seemingly show her attraction to his body and her will to give him some physical pleasure (another signal to underscore that a "complicity" between them was surfacing).

As for my own poll, I personally believe in those few seconds she kept rubbing Batman's flank: Catwoman probably felt that right there the batsuit was dangerously thinner ("there you are" really meant "I've just found your weak spot"), so she "tested" that area a little more, just to be sure... By doing so, she created an arousing sensation that Batman briefly enjoyed before being stabbed...

My only unanswered question is this: even though he was being charmed by Catwoman, could Batman in some way have avoided her final assault? Or was it inevitable given the circumstances? 

[Catwoman]

it was inevitable. even batman has a brain and a penis and only enough blood for one at the time.

[Catbat]

it was inevitable. even batman has a brain and a penis and only enough blood for one at the time.

Hahaha Catwoman!

My idea is that Batman had very few chances to leave the balcony unharmed because, apart from your anatomical analysis, he was overconfident and didn't take Catwoman seriously. For instance, he didn't consider that her claws could actually pierce his batsuit and at one point he also seemed to expect her to gratify him sexually...
Fortunately Catwoman brought him back to reality!