From what I've seen, it is not carrying a bunch of compressed air (which makes sense given the depths where they are going to have to mix all sorts of gases, plus the weight would be unsustainable). Nuclear subs create air to breath by separating O2 from the seawater, but that is only possible because they can produce so much power with the reactor, don't think that's an option for a vessel that is running on batteries. So, they are likely using a closed circuit rebreather type setup. I'm not an expert on those, especially in a sub like application, but the general theory is that small bottles of gases (the air we breath is only 18% O2, and we only use a tiny bit of that with each breath, so they carry straight O2 and add small amounts back in through the process) to supply air and then recirculated through a medium that is a lot like kitty litter to capture the CO2. The limiting factor is the amount of O2 AND the filter medium which will eventually saturate with CO2. What I don't know is if the system they use requires power (likely it has sensors adjust the inputs that do at least) or is passive like an old style SCUBA Rebreather where the operator adjusts the mixes manually. If they had a failure and lost power as part of why they lost comms with the support ship, they could have lost their air supply very quickly or if there was an issue with the gas mixing, they could have all been impacted by CO2 poisoning or Nitrogen Narcosis (Narc'd) which would make them loopy and who knows what someone would do wrong in that state, or too much O2 which can kill you when in a pressurized environment. (Link below is how a rebreather works if you're interested) So many potential failures in an environment where a tiny failure is likely catastrophic.