Personally, I think the phrase should be punctuated like this:
"United, we stand; divided, we fall."
The thing is, I could envision "United we stand" without a comma perhaps because it's often used as a declaration/affirmation.
However, it's the second part that gets me because something about the placement of "divided" in the front of "divided we fall" makes me feel like a comma is required after "divided" and so in the interest of maintaining symmetry, I also inserted a comma after "united".
I have a feeling it's because "united" and "divided" are serving two different purposes within their own clauses, that is, "united" is being used as an adverb while "divided" is more like an answer and clause of its own (in response to the implied question of "Why did we fall?"), so that while on the surface, the two may simply appear to be modifiers, one is actually something more.