Native speaker (Brit in USA) here. Either one is fine, although they have subtle differences in meaning and implication (to me) in this context.

The first thing that struck me before I gave this any real thought is that "How" here connotes a little incredulity or even amazement (to me). There's an implied, rhetorical sense of unlikelihood of the fact. ("How are Rome's monuments still standing?! Shouldn't they have fallen down by now?")

"How" also implies (to me) that we seek an explanation of processes, means, techniques, or methods. It invites an answer that's somehow more dynamic and more detailed. "Why" is asking "for what reason(s)?" The "Why" version of the question feels more direct, but the answer space is broader and more abstract. "How" feels, forgive me, more concrete here than "Why" :)

How -> explain the processes, techniques, or workings. Why -> explain the reasons/causes. Obviously, there's overlap there, and the distinction is subtle, so perhaps some of this is only in my head :)

I found http://www.differencebetween.net/language/grammar-language/d... which seems to half-agree.

How and why sound to me like slightly different questions and the best one might depend on the answer.

"Why is something still standing" could be circumstances related - eg all the other ones got demolished except this one for reason x, or y group of people stepped in to maintain it etc

"How is something still standing" sounds more like the method for it standing - eg the structure had some extra cross bracing on the lower level etc

Maybe it's just me :)

They sound the same to me (native American English).

'how' sounds a bit wrong to me, too. But it's popular in the USA.

Either reads fine to me.