As an example:

Let's say your opponent's character was equipped with this and chose Impervious. You attack and by some means(1 Pen, 3 normal w/o Imp. roll, etc.) cause your opponent to take 1 click of damage, but you also deal knockback, and your opponent does not have an on-dial reducer and is knocked into a wall.

I assume once they click the damage, they lose the Impervious, as their selection only lasts 'until clicked'. However, they also get to re-select a power 'after clicked'. Will they be able to re-select a reducer after clicking the damage but before resolving the knockback?

Interesting question ...

And also an easy one to answer. Yes, they get to choose as soon as the dial is clicked, which is going to be before any knock back happens. Just obviously keep in mind that knock back is checked for when the attack hits, before the damage is taken, so you couldn't pick Charge or something (like on Eclipso, for instance) to try to ignore the knock back.