This seems related to the concept of Last Thursdayism - if the world was created last thursday, how would you be able to tell the difference?
You have some memories of earlier times than last thursday, but there's literally nothing that prevents them from being indistinguishably fake; your consciousness could be existing in a simulation that started five seconds ago, and there's no way to disprove that.
But the reasonable answer to that is if it's not possible to tell the difference, then we define that to be the same consciousness; so that the answer to the question "if we are not only not the same consciousness after we fade away by daily sleep, etc.., but we are constantly fading away in short cycles" is "it's the same consciousness, period" by definition.
You have some memories of earlier times than last thursday, but there's literally nothing that prevents them from being indistinguishably fake; your consciousness could be existing in a simulation that started five seconds ago, and there's no way to disprove that.
But the reasonable answer to that is if it's not possible to tell the difference, then we define that to be the same consciousness; so that the answer to the question "if we are not only not the same consciousness after we fade away by daily sleep, etc.., but we are constantly fading away in short cycles" is "it's the same consciousness, period" by definition.