Falling down on can be replaced with numerous synonyms such as failing, disappointing, letting down, dropping the ball, underperforming, floundering, deteriorating, declining, or collapsing. Using such synonyms can help add variety to your language and express the concept in a more precise manner. For instance, instead of saying "he is falling down on his responsibilities," try using a synonym like "he is underperforming in his duties." It not only enhances the impact of your words but also makes them more engaging. Thus, using synonyms for falling down on can help you communicate more effectively and accurately.