I have some sympathy with the "garbage in, garbage out" approach to translation. Since "punto arcóntico" is more or less nonsense, it would serve the author right to translate it by the equally nonsensical expression "archontic point". But tempting though it may be, I really don't think we can do it.

That's not to say that "archontic" is meaningless in itself, though its meaning is somewhat elusive. But it certain has nothing to do with this context. "Archontic" really means "relating to the archons", magistrates in ancient Athens. But it's been hijacked by various obscurantist tendencies. On the one hand, in Gnostic thinking archons are alien beings that penetrate the human mind (or something like that). And Derrida (bless him) adopted the word, relating it to the idea of the archive; from this we get to the idea of an "archontic" text, which is really another way of saying an intertext (I think). Here's more info. if required;
http://www.bibliotecapleyades.net/vida_alien/alien_archons02...
https://books.google.es/books?id=UgZsi_DOKoQC&pg=PA64&lpg=PA...

But none of this has anything obvious to do with our context. As far as I can see, "punto arcóntico" is an expression originating in Argentina, and the idea seems to be that "arcóntico" is related to "origin" (arkhe in Greek). It may very well come from Derrida (after all, who really understands what Derrida was on about)?

"En parte, la naturaleza de este proceso dependerá del balance de fuerzas que le den origen, de lo que los grupos en contienda o los responsables estén dispuestos a admitir. Es, en otras palabras, un instante arcóntico, en la acepción de Derrida, un instante que establece el origen, un arkhé (Derrida, 1995), la constitución de un archivo."
http://biblioteca.clacso.edu.ar/clacso/becas/20150131091650/...

So really I think what they mean is a point that is at the origin of the question. So really it amounts to nothing more than a pretentious and fancy way of saying "fundamental" or "primordial".

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Note added at 49 mins (2016-02-09 19:49:33 GMT)
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As far as I can judge this is what people mean by the term when they use it in this kind of context. This is on judicial reform:

"La cuestión demandará entre diez y quince años de trabajo arduo y perseverante, para recobrar los niveles adecuados y contribuir al restablecimiento de la seguridad jurídica, que es el punto arcóntico de la cuestión."
http://www.lanacion.com.ar/507835-hay-que-definir-las-politi...

This one's about finance and credit (it's by a university law professor, who I suppose is professionally obliged to sound clever):
"Tal ausencia de transparencia existe y erosiona la confianza, tema arcóntico en el otorgamiento de crédito."
http://www.catedra-piaggi.com.ar/biblio/biblio22.html

The very same learned law professor, this time talking about arbitration:
"Adicionalmente señalan la conveniencia de pactar el grado de confidencialidad –aspecto arcóntico del arbitraje– que las partes y los árbitros deberán guardar"
http://dspace.uces.edu.ar:8180/xmlui/bitstream/handle/123456...

But "archontic" doesn't seem to have crept into English legal language in the same way, for which I suppose we should be grateful.