One Week Friends Vol. 5 (manga)

Hearing Hajime's story about the friendship he once shared with Kaori leads Yuuki to help reunite the pair. With a new old friend now in the mix, Kaori needs more than one diary to avoid starting every week from zero. But when Hajime and Kaori start to display a special bond that can be shared only by longtime friends, Yuuki is forced to wonder exactly what sort of relationship he wants with someone whose memory of him lasts only so long...