Takaki and Akari exchange letters throughout middle school. However in the second arc for some reason they stop communicating without any reason? This is even more bizarre given cellphones are commonplace by the second arc. Looking back at the movie, Takaki spends all his life after the first arc moping about Akari without making ANY attempts to communicate with her, despite being able to do so fine in middle school.
It's shown in the third arc's montage that, as happens with many relationships, they just gradually grew apart - the letters grew farther and farther apart, until they stopped entirely as the two grew up. It's likely that the letters had stopped before the two of them got cell phones.
