I think it's a little more complicated than that. In a 50 First Dates type of scenario, their ability to form certain types of memories is damaged, not non-existent. And I would argue that with enough brain damage someone like an extreme lobotomy victim may stop being considered conscious.
I’m not familiar with 50 First Dates, I was thinking of cases like Clive Wearing [0]. I would agree that consciousness requires some sort of ultra-short-term working memory, but I also think that mechanisms similar to CoT loops can conceivably fulfill that role. Today’s generative AIs consist of more than just the static network-of-weights model.
[0] https://en.wikipedia.org/wiki/Clive_Wearing#Amnesia