The second clause is translated as some version of: "If you look at it from the point of Change, then heaven and earth never stay the same for even a moment".

Here's what I think I know:

不 negates a verb
能 indicates that something is possible, and functions as an auxiliary to another verb
不能(verb) therefore means "cannot (verb)", "does not (verb)"
以 has a variety of meanings, but the only one that fits here is to indicate a period of time: 一瞬 ("a moment", "the blink of an eye").

My question is this: what verb is 不能 modifying? What in the verse conveys "to stay the same"? Is there an implied verb somewhere meaning "to be unchanged"? How is the above interpretation derived, exactly?

Many thanks to anyone who can explain this to me.

I should mention also that I first encountered this in its literary Japanese form, where the full gloss is: 蓋し将た其の変ずる者よりして之を観れば、則ち天地も曾て以て一瞬なる能はず, if that helps anyone to understand the issue. There is no verb explicitly indicating "existence", "stopping", or "lack of change" in the Japanese interpretation either.