He kept refusing my help and insisted on solving the problem himself.

refusing 是动词 refuse 的现在分词形式。refuse 由前缀 re-（表示"反对、反向"）和词根 fuse（来自拉丁语 fundere，意为"倾倒"）组成，字面意思是"倒回去"，引申为"拒绝、不接受"。