Despite evidence to the contrary, she kept insisting that she wasn't late.

insisting 是动词 insist 的现在分词形式。insist 由前缀 in-（表示"加强"）和词根 sist（来自拉丁语，意为"站立"）组成，字面意思是"坚定地站着"，引申为"坚持、坚决主张"的意思。在这里 insisting 表示"持续坚持某种说法或立场"的动作。