One synonym for the word "downfalling" is "decline." This refers to a gradual decrease or deterioration over time. Another synonym is "collapse," which suggests a sudden and complete failure. "Falling apart" is another similar phrase, indicating that something is disintegrating or falling into disrepair. "Lapse" is a more subtle synonym, suggesting a temporary or partial loss of progress or success. Finally, "defeat" can be used to describe a situation in which someone or something has been overcome by an adversary or obstacle, leading to their downfall.