This is the 15808th most frequent Russian word.
продолжавшейся
"Продолжавшейся" means "continuing" or "that was continuing."
The word 'продолжавшейся' is used as a past participle with a feminine noun ('история'), implying an ongoing action in the past.
История, продолжавшейся веками, наконец, закончилась.
The story, which had continued for centuries, finally came to an end.
Here, 'продолжавшейся' acts as a descriptive participle for 'война', indicating the action related to the subject in the past tense.
Война, продолжавшейся столько лет, оставила глубокий след.
The war, which had lasted for so many years, left a deep mark.
In this sentence, 'продолжавшейся' describes the subject 'дискуссия', denoting the action extended over time before the present.