Usagi ga Nihiki 

Endowed with immortality, Suzu Inaba has lived for 398 years. Her daily routine consists of getting Sakuro "Saku" Usami, her 19-year-old live-in boyfriend, to help her kill herself. But every time Suzu wakes up from another failed suicide attempt, Saku begs her to continue living with him. One day Suzu, haunted by painful memories, hits on a surefire way to die. A tale of eternal love between two people whose differences grow even as their love deepens.