This is the 7385th most frequent Chinese word.
苦苦
Persistently; arduously; painstakingly.
Here, '苦苦' is used to describe the persistent and struggling effort in '思索' (pondering).
他苦苦地思索答案却找不到办法。
He pondered desperately for an answer but could not find a solution.
In this sentence, '苦苦' emphasizes the depth and emotional intensity of the begging '哀求'.
她苦苦哀求他们停下但没人理会。
She begged desperately for them to stop but nobody paid attention.
'苦苦' in this context describes an arduous and continuous effort '奋斗' (struggle) to achieve a goal.