To my knowledge, interfering with the healing factor only works while actively interfering it, and if you stop at any point Logan is able to come back essentially post mortem. In some books it is so powerful that he essentially stopped aging when he acquired the healing factor secondary mutation. In the movies, he still ages but much slower, and eventually his body begins to reject the adamantium in his skeleton and his healing factor cannot heal fast enough, leading to his (kinda) death.