If a party suffers defeat, all of the heroes in that party will come down with a bad case of Maze Sickness. Sick heroes will no longer able to fight in the current maze. As a result, you won't be able to use them again until either the Dark Maze reshuffles as it does every three weeks or you start the maze over again, thereby resetting your progress.
But worry not! You can always form another party with heroes who haven't fallen ill with Maze Sickness in order to continue your journey into the maze's depths.