Because if we do not find our objective and perform our task before the time limit, the Trumps will punish us when we return. They have a habit of making Liminal Space into extremely harsh or mentally taxing terrain when we "displease" them. Given how physically, emotionally, and mentally exhausting the Jaunts are anyway, it is no good to refuse.

If you won't help fro the sake of the rest of us, then at the very least help for your own sake.

... furthermore, these people continue lives past our departure. What we do affects each world we've visited. I want to help them, and I am sure many on the Network agree with me. They deserve that much, if they're to be sucked into this twisted game with the rest of us, even if only for a while.