After a week of friendship with Hase, just as expected Kaori remembers nothing of her classmate's status as a new-found friend. Shock to the system though this might be, Hase has no intentions of giving up and thus starts all over again by asking Fujimiya to be his friend.
This request out of the blue (from her perspective) doesn't exactly go down well, but as she realises that she has no recollection of her lunchtimes from the previous week it becomes clear that something precious to her must have happened during those breaks - thus, she comes to realise that Hase was indeed her friend of the week before, and as a result she once again allows him into her life.
Forewarned is forearmed in Hase's case, and to avoid a repetition of these events he suggests that perhaps Kaori should keep a diary (why has nobody suggested this to her before?!) - something which she dutifully does, chronicling every little thing from Hase's preference in sandwiches through to an abortive visit to a crepe restaurant than instead turns into an enjoyable karaoke session to end the week. Armed with her diary and a note telling her to read it before school (complete with a reminder that Hase is her friend), Kaori is all set to start a new week, although it's not her own difficulties but Hase's expectations that prove hard for her to bear...
While One Week Friends could have been filled with huge, overblown drama, there's a serene subtlety to what it relies upon instead - after bringing Hase and Fujimiya together again for another week of enjoyable chit-chat and a day about, it makes use of quiet, understated moments to reveal Kaori's pain regarding her situation, be it the knowledge that memories of an important day for her with vanish or (perhaps more notably) her desperation to please Hase by assuring him that she hasn't forgotten everything about him even if it isn't the least bit true. Whether the series can continue in this vein throughout is another question, but for now it's a pleasing way to frame the series helped along by characters who you can't help but warm to, making it a far cry from the recent Golden Time in its handling of a similar (although far from identical) subject.