I think before we can delve into this question, we first need to define reality. If we want a dictionary definition: "the world or the state of things as they actually exist, as opposed to an idealistic or notional idea of them." So then, does that mean that to live in reality, one must live chronologically? Barrymore is aging physically, but mentally she regresses back to that same day and age, reliving the same events of that day.
It effects her, it effects her future, and it effects the way that she is able to be an active member of society. Without the help of her father and brother she would have extreme difficulty functioning in everyday life. Eventually Adam Sandler's character creates a video addressed to Barrymore telling her about her amnesia, she watches the video each morning and each morning she has a different reaction-- sad or angry.
Since she has different reactions, does that make her more real? She is still a person and her daily encounters are still real, she just can't remember them the next day. If she is consistently going back tot he same day, then she is not able to keep up with the current events of the community or the state or the country, which is why her father and brother print out copies of newspaper from the day she suffered the accident causing amnesia. Essentially, she does not live in reality. She lives "a" reality, just not the same one as everyone else.