One Week Friends

Kaori Fujimiya is always alone because all of her happy memories, including time spent with her friends, disappear every Monday. Deciding that he wants to be friends with her anyway, Yuuki Hase tries to get close to Kaori each week, wishing that she would one day call him "a friend."
(Source: MyAnimeList)
~~ Adapted from the manga series "One Week Friends" (一週間フレンズ。) by Hazuki Matcha (葉月抹茶).