Elementals usually have a certain amount of energy they use to keep themselves together, when this energy is depleted the just stop being animate. It isn't really about losing material (chop a water-tentacle off and it just reconnects), but about losing energy. Every time you make the elemental have to put itself back together, or restart itself (an air elemental spinning up again or a fire elemental bursting back), it uses up energy. But it also uses energy to move and attack, but usually not as much because it has balance (equilibrium, cohesion, structure, tension, in-whatever-shape-it-finds-easiest-to-use). So an elemental would actually be a valid creature to give a kind of "hit point bar" of energy, with normal damage for state changes. This means that elementals cannot be killed by lucky hits, cannot be debilitated, and cannot be killed by a single stray arrow.
I'm not sure where elementals would get more energy or survive any length of time, they usually require a pure magic source of some kind. This does not necessarily require the magic arc, as one could use a placeholder that allows elementals to simply regenerate when in their own element, with an excuse like "draining kinetic energy" (wind, water), "draining heat" (fire elemental in magma), or "decomposing contained material" (earth).
I do recall one story that was describing a "windigo" in which the creature of air simply picked up a person and disintegrated them with winds significantly faster than the average tornado. The creature was slightly visible for a while, then it would need another person...
As before, an earth elemental is far more likely in the placeholder to need to eat than an air elemental. One would expect if some entity was a living in a certain quantity of matter it would have abilities over that matter which transcend normal reactions of life. So it might be able to drain types of energy going through it to store as magical energy. Elementals might even become an important and rare resources that allows transformation of normal energy types into magic energy, if you can convince/coerce them that is.
I didn't think swarms would work that way, I thought they just had an insanely high ability to dodge from the small size of the bugs.