After months of intense competition, their determination was finally worn down.

worn down 是动词短语 wear down 的过去分词形式，wear 意思是"磨损、消耗"，down 表示"减少、减弱"。wear down 合起来表示"逐渐削弱、消磨"的意思，在句中表示被动含义，指"被消磨殆尽"。