So, some people have complained a bit about some quests giving the Overlord a chance to keep knocking out the heroes to draw his entire deck before moving on to the second encounter, or otherwise stalling the game for some reason. So, I've come up with rules for the heroes to surrender the first encounter of a quest:
After three full rounds have been played, the heroes may surrender. They must surrender at the start of the hero turn, before any heroes act. The current encounter immediately ends, and the Overlord gets the best "win" possible (for example, in A Fat Goblin, if the heroes have stored one crop, the overlord's stolen one crop, there's another crop still on the board, and a fourth crop being held by a hero, the overlord will end up with 3 crops; he won't get the one the heroes already stored, but he will get the one still held by a hero). The overlord draws two cards, and any search tokens still on the board are lost.
And to keep things fair, if the overlord wants to surrender:
At the start of any overlord turn, before any cards are played and any monsters activated (but after drawing his card for the turn), the overlord may surrender. His turn immediately ends, and the hero players get one last turn before the encounter ends. The heroes get the best "win" possible (to use the Fat Goblin example above, the heroes won't take back the crop the overlord already took, but they do get to keep the two on the board and the one they already stored). For each search token on the board, the heroes pick one hero to search it.
Now, for a bit of reasoning why I picked these rules:
For the heroes surrender rule, part of the first encounter for the overlord is getting to beat up the heroes a bit before the second encounter. Thus, the heroes have to go through at least three rounds of being beat on before they can push forward. To keep the heroes from just declaring a surrender freely when they think the're "good enough", the overlord also gets some extra cards.
I imagine the overlord surrender rule won't come up as often, but in some encounters it's possible for the heroes to stall long enough to heal everyone to full before the encounter ends. The heroes do have a "time limit" in the form of the overlord drawing more cards, but this way the overlord can keep from giving the heroes infinite time to heal. Since damage dealt by heroes doesn't carry over like damage dealt by the overlord is, there's no reason to keep the overlord from surrendering right off the bat; the heroes do get all the search tokens, after all.