Bai LiHua had a strict training routine for himself as well. Though since he already had a formed spiritual core, he only had to revitalize it everyday, to be in his prime condition. The core cultivation method that the Bai clan uses is unique to only them. With their method, once a spiritual core is formed, the person stops aging with their bodies. So essentially, until a person's spritual core is not destroyed, a member of the Bai clan cannot die.
Most cultivators use different methods to prolong their lives, but it doesn't mean they are immortal. Same is with the Bai clan's method. The method itself has a drawback, which is that once you strain your core more than it allows, even in a moment of need; the core will be damaged. The same happened with the Clan Master, Bai Shinzhou. Once his core was damaged, it couldn't be mended. So either Bai Shinzhou could cultivate a new core, or he could die in a mildly painful manner; by the curse of aging.