Okay, so it's almost like the "running out of supplies" bit is just an in-game way of tracking your progress in the Expedition questline.
As long as you are not abusing supplies (like giving them all away to the pirates), the amount just slowly trickles down, until they are critically-low by the time of the last quest.
I responded to every invasion mission (there were like 8 of them) and only 2 people died on my watch. By the end, there were 25 people, almost no supplies, and almost full jetski complement. [I guess jetskis don't deplete as quickly as other supplies, if you don't give them to the pirates.]
There really should be a quest to get more supplies for the Expedition, though, if you are willing to. In Fallout, you could buy water from merchants to extend the water chip quest timeline. (It even had the consequence of speeding up the mutant invasion of the vault, because they would learn your location more quickly).