I also feel like Sam probably did give up- for the moment. The desperation and the grief was pretty much bursting out of him in the last episode. But it's not for long. I think he just hit a wall when he killed the Crossroad demon, but I think something will spur him on to start looking for other means to get Dean out of the deal. I don't know any spoilers, so I could be wrong, but I just don't see Sam giving up completely. Not for long, anyway.