This idea, that the creation is re-created at every instant is not found in Chazal or Rishonim. It first shows up in the above referenced Nefesh Hachayim. It is sort-of self understood within the framework of Kabbalah or Rambam ideology. If existence itself is lent from Hashem then it is a constant act of perpetuation of existence. This is applied to the Pasuk, בדבר ה’ שמים נעשו, that the substance the world is made from is D’var Hashem.
This is a fine idea, but not essential to Judaism or the Torah. It is also, seemingly, an idea that was taken a bit too far. In fact, denying the function of Sheshes Yamim might truly be undermining the Torah. As we know, keeping Shabbos is like keeping the whole Torah.
So, while pondering the lofty concept of how the whole existence hangs on, and is made up of, D’var Hashem, let’s not lose sight of the basic idea of ‘creation’. Rules of nature were crafted and the world was formed back in Sheshes Yemei Bereishis. Existence was lent and is continuously breathed from then on.