You don't need to explain why
Big frame-challenge incoming, as I'll be saying you don't need an in-world reason. But first, let me answer strictly your question before tackling the underlying issue: If you really do want to add in-world reasons, you only need to throw out some random explanations, and that'll work. I mean, if morphine allows you to still run and shoot with broken legs, and you can revive bleeding out teammates just by giving them your hand1, almost anything will work just fine 😊.
This leads me to my frame-challenge: You don't need an in-world explanation for your game mechanic in the first place.
Throughout the existence of the gaming industry, game mechanics are most of the time akin to premises in worldbuilding: You set the rules, and people will gladly accept them as long as they're entertaining and consistent with the other rules. Then, if it's wanted, game-mechanics are explained in-world by just some techno, magicko- or bio-babble without going further onto it. And it works very well.
How you implement how characters (cannot) die is especially one of the kind which is tolerated by the gaming community. To give you proof of that, see some of these game worlds below that pulled that off very well. I'm quoting examples from more story-driven games for the purpose of building a narrative-intensive game, but it happens virtually everywhere:
- In most recent occidental RPGs with player parties, you don't die in game battles easily, if at all: The Banner Saga, KOTOR, Mass Effect… No explanation is given for this. In fact, if and when to die is one of the settings you can alter in the Pathfinder and Pillars of Eternity video game series. No in-world explanation there, either!
- Speaking of RPGs, somehow in Final Fantasy your characters never truly go down even after having been pierced by 10,000 giant cactus needles… Until their dramatic cutscene comes in (e.g., FF7).
- All recent Elder Scrolls and Fallout have unkillable, essential characters, which is one of their famous trademarks. They will just need to take a breath, even after you fire at them with an atomic rocket launcher. Rarely, they die but resurrect just to annoy you once more.
- Dripping into horror, the Resident Evil series has a good amount of antagonists who just don't feel like dying yet. Sometimes, the main characters make snarky, almost meta comments about that.
- All of Telltale-like games' deaths are scripted. Therefore, first, they're not really happening in actual game sequences like you ask1. Then, characters' lives are more tied to the story's needs than the world rules. They live just enough to set a cliffhanger, for instance.
Ok, it was left unexplained with success before, but is it a problem if I do it in my game?
I'll end with a special game which will serve as the conclusion of my worldbuilding+game design advice. In Celeste, the principle of dying and coming back as if nothing happened is not explained at all from an in-world perspective, but it makes the most sense to showcase how Madeline—the protagonist—feels. This is a clear intent of the game designers, something you are told as soon as you change the difficulty3. They tell you they want you to die and fail with a purpose in mind: face the hardships the character is feeling and create one of the strongest bonds you can ever make in games. Explaining it would actively prevent transmitting this feeling: You'll just end up tripping over yourself and go in lengthy but uninteresting details rather than focusing on the game pillars and unique selling point.
That's what makes an excellent, lively-relationship between your game and its world. The most well-made games create game loops, character controls and game mechanics to further enhance the world and story they're depicting. It's so that players don't see the world, they feel part of it.
This means that sometimes you have to allow yourself to not explain game mechanics when it would muddle up (or worse, contradict) the themes and messages you want to explore with your story and world. From the description of your question, this seems exactly like one of the cases where you shouldn't be spending your and your players' time on that.
So understand that most game rules are already-accepted premises you don't always need to explain through the world. Not everything in the world your player will experience need to be fully rationalized, and that's fine actually. Good game worlds don't explain everything about what is happening in the game, because the world is not the game. In fact, good worlds in general don't explain everything to the minute detail, be it for novels, comics or movies. The world shouldn't prevent you from keeping the player characters alive, nor is it always necessary to call for it if this your game-design decision.
1: The list of cooperative games doing this is sooo long. I'll just take a few from my basket: Borderlands, Left 4 Dead, Full Metal Furies, Aliens: Fireteam Elite, Helldivers...
2: I absolutely mean no offense to these adventure/point-and-click game mechanics, but QuickTime Events (QTEs) and single-click cutscenes pale in comparison to the battle system you're apparently designing.
3: As far as I remember, a pop-up appears when you get in the assisted mode to get more jumps or plain immortality.