Hyphenation of non-combat-related injury

Short answer: They're both acceptable, as is "non–combat related injury" with an en dash. If you're a stickler for typographic difference, you might well favour "non–combat related" over "non-combat related".

Long answer:

Starting with combat-related/combat related first, to use that as a starting point: In combining combat and related we create a new modifier that acts as an adjective. For such compounds we may or may not hyphenate, to create hyphenated compounds or open compounds respectively.*

In deciding which to go for, the main thing to remember is that the point of the hyphen is to indicate to the reader that the two words form a single modifier. The more likely they are to misread it otherwise, the more we would want to lean toward hyphenating.

We would never hyphenate a proper noun or adjective ("North American writer", not "North-American writer") and we never hyphenate adverb-adjective pairs where the adverb modifies the adjective ("surprisingly long explanation", not "surprisingly-long explanation", at least not since the 19th Century).

We would probably not hyphenate a pair of words that formed a familiar term in itself ("high school sports" not "high-school sports"). One way to judge is to consider whether you'd be surprised to find it standing on its own in a dictionary or encyclopaedia (more so than whether you actually would find it - they can have some obscure things sometimes!).

We would definitely hyphenate something that could easily be interpreted differently without the hyphen ("a man-eating tiger" is a dangerous thing, but "a man eating tiger" is putting novel gastronomic experience above concerns for endangered species).

In between there is much more room for personal preference and disagreements.

My personal approach is to consider if I'd glanced at it and saw it from half-way through the modifier would I misinterpret it as something very wrong. I might take "resistant coating" to be some sort of coating that generally made the item it was applied to more resistant to wear, tear and staining, so if it was part of "fire-resistant coating" I would hyphenate it. If I saw "related injury" I would wonder "what-related?" and scan back, so to me "combat related injury" is fine.

Again though, that's just my personal approach to the cases where either choice is valid. I wouldn't argue against other choices, and some style guides might have something to say on the matter.

Now, when we add non, we are creating a compound out of terms where one is already a compound. Here we normally use an en dash for the further compounding: "pro-privatisation–anti-privatisation debate", "Turner Prize–winning artist".

But non is a prefix that is never used on it's own, and in this case, if the compound we already have is hyphenated, then we would almost never use a dash, as the longer symbol with the short item that isn't a full word followed by the shorter symbol, can be visually distracting. Also, some people just simply don't bother with en dashes in the open compound case, either.

So, for the positive form (without the non) we can have either of:

combat related injury

combat-related injury

And for the negative form, we can have either of:

non–combat related injury

non-combat-related injury

And if we just don't care about figuring out how to type a dash on a given computer:

non-combat related injury

Is okay too.

But

non–combat-related injury

is questionable.

(FWIW, I'd go for "combat related" and "non–combat related").

*There are also closed compounds like dishcloth, which complicates things even more. Luckily, since these are normally a compound of two or more nouns that create a new noun, we don't need to consider them here.