Is a person with narcissistic personality stable or the problem changes a lot over the years?

Mostly stable. Personality disorders tend to remain as such unless there is some kind of intervention. Personality disorders have characteristics that therapists refer to as "ego-syntonic, " which means that others recognize their characteristics as problematic but the person herself does not! The goal of therapy is to render ego-dystonic what had once been ego-syntonic for the patient.
Narcissism. Stability is not really the issue with narcissists. Eventually they drive away people close to them, alienate bosses and subordinates, and I general cannot bring themselves to being able to address their own part in their own misery. Intensive psychotherapy is typically needed, and over a long period of time. In my opinion, psychoanalysis is the best way to go.