Even though learning English was hard, he stayed persevering in his studies.

persevering 是动词 persevere 的现在分词形式。persevere 来自拉丁语 perseverare，由 per-（彻底）和 severus（严格的）组成，意思是"坚持、不屈不挠"。 persevering 在这里作形容词用，表示"坚持不懈的、持之以恒的"，描述他学习英语时的态度。