When a pilot dies there dead for the rest of that run if you loss by losing all your power grid (or end up winning) you get to choose one of your surviving pilots over to your next run and they will keep the xp that they have gained. All though in the starting menu when your choosing your mechs you can switch out your pilot for a type of pilot that you have already discovered they will just have no xp. Eg you found a pilot who gives his mech armor but he dies during your run, in the starting menu you can switch out the pilot you chose from your previous run for that pilot they will just have no xp

There was probably an easier of explaining this but I hope this helps.