Here is the complete sentence:
Numerous collections of short stories include works by Isaac Bashevis Singer who, despite living in the US for more than 15 years, continued to write primarily in Yiddish.
If it were just despite living in the US, it would all just be fine. But the years indicate that he has been living there for sometimes. So I feel that despite having lived in the US for more than 15 yrs would be more correct.