Does frigid touch with mel newly awaken -1 might for each time its chooses or once for the spell cast on a single unit?

Per time it chooses — not once per spell. With empowered Mel, Newly Awakened, each execution of Frigid Touch's effect gets the extra −1, so repeating on the same unit stacks to −6 total this turn.

Repeat makes the spell's instructions execute a second time (Rule 820.1.d), and each execution is its own "give −[S] to a unit" event. Mel's Empowered ability is a replacement effect that applies to each of those events individually (like the Moonfall ruling, FAQ #11737), turning each −2 into −3. So one cast with Repeat on a single unit = −3, then −3 = −6 Might.

Worth noting: the −6 is treated as 0 Might for game purposes, and this still doesn't kill the unit by itself — it only dies if it has damage marked equal to or greater than its current Might.