He tried his best to listen to Snape despite his turbulent emotions. With Snape clearly trying desperately and discreetly to save him, it felt disrespectful for Harry to not at least try and help him succeed, even if Harry had little faith in the likelihood of a positive outcome. If this new regime worked, Harry might never have to tell Draco about the fatal nature of his wound, and that thought alone was enough to ensure his intense concentration.