It's another one of those areas that could do with some more thought - at present, injury is based on critical
IIRC, there is also Resilience check against getting an injury. Or at least it's not on every crit. If you want some ideas or feedback at the time of thinking, feel free to let us know.
So blocking the KO through the perk would also block an injury, if one is applied on KO.
Ok. Understanding more now. It's not like a re-spawn mechanic, but more like when you sustained a blow that would otherwise knock you down, right?* Except it's not your personal lucky star but Arcadi's commanding presence at play. And indeed KO related things won't apply. However, in that case let me provide some different take:
No problem with bursts. Actually, bursts are logical defense against the thing. Depends on presentation. For example, barking can let us know what happened (perhaps Arcadi barks a command and the ally responds, plus/or some red text like 'Withstood downing!'). It can simply activate once per battle per ally. And Arcadi's perk icon on the top left can have 4 parts, a part for an ally grays out upon use. No need to complicate the burst code, neither applying unnecessary status icons. Btw. combining a shotgun + exploding canister applies two damages too, so...
Have you considered giving the perk to some of the enemy leaders? Or a drug having this properties (on districts under Elysium facility influence). Then I would for sure arm the team with smgs and other low AP+low dam means for such tricky encounter. The thing is, now the burst works for us...
Ad*: what about changing the name to make it more clear, eg. "Stand fast" -> "Steadfast" (sorry if stupid, non-native speaker here).