Well I can make a hypothesis that the human brain will not be able to easily forget centuries worth of memories given the thing that after a certain age people often report having clearer memories of longer ago events than newer ones and that these memories will come back to them periodically, will over time the long term memories be filled up?

my personal feeling would be no, you will keep getting that memory of the person you liked in high school when you're 600 but your probably won't remember anything particularly clearly past 20 years before and the stuff from your 70s-80s will be totally gone.