Rin: Daughters of Mnemosyne (2008) - Mnemosyne－ムネモシュネの娘たち－
For normal people, getting stabbed to death would constitute the end of the road. For Rin Asogi, it's a mere inconvenience. Rin is immortal, a nice perk to have when you're a private detective constantly finding yourself in dangerous situations.
Rin has eaten a "time fruit": a fruit from the guardian tree Yggdrasil, which, when consumed by a woman, makes her unable to die. Rin's immortality doesn't stop others from trying to kill her, of course; over her long lifetime she has been shot at, cut up, maimed, tortured, and suffered countless other violent deaths.
This time, it's different. The year 1990 sparks the beginning of a series of events in Rin's life that sends her spiraling toward her fate. Someone is hunting down immortal women like Rin, and Rin's life may be in actual danger.
Mnemosyne no Musume-tachi spans 65 years in Rin's life, during which she watches those around her get old while she herself remains unchanged. Higher forces are after her, and Rin must use every means at her disposal—or her next death may just be her last.
And it all begins when she goes searching for a lost cat, but finds the amnesiac Koki Maeno instead...