Quiz question confusion

Question

"Ella ha roto con él pero ________ así él sigue insistiendo.

She broke up with him but even so he keeps trying.

(HINT: aún or aun?)"

I've already forgotten which I picked, but I got it wrong. My confusion is that according to the lesson, both "aun así" and "aún así" mean "despite that". I can't think of a sentence in English where "even so" is not interchangeable with "despite that". It certainly seems like they are interchangeable in the quiz question above. Is there a nuance that I'm not grasping that explains why only one of the options is correct?

Accepted Answer

Hola R
The answer here must be "aun así" (no accent on aun)
What we say in the lesson is that you can find both "aun así" and "aún así" but meaning different things:
"aun así" means "even so" or "despite that", which is what we express in this sentence from the quiz:

Ella ha roto con él pero, aun así, él sigue insistiendo.
(She broke up with him but even so/despite that, he keeps trying.)

"aún así" means "still like that" so we could have this sentence for example:

¿Estás aún así? ¿Sin maquillar? Vamos a llegar tarde a la fiesta. 
(Are you still like that? With no make up on?  We will be late to the party.)

This aún could be replaced by "todavía": ¿Estás todavía así? 
I hope this clarified it.
Saludos
Inma

Answer

I think the thing that confused me is that you put this example: "Me pagarán poco dinero, pero, aun así, aceptaré el trabajo.

They won't pay me a lot of money, but, despite that, I will accept the job"

in the "aún así" section, even though it's spelled "aun así" in the example. If this was intentional, I can't see why because the two sentences don't seem to relate to each other.

Answer

Hola R
Sorry, yes, there is no mistake in the usage of aun así, but that example was placed in the lesson in the wrong box. I understand why it was confusing. I placed it in the right box. 
Saludos
Inma