Inveterate, confirmed, chronic, deep-seated, deep-rooted are comparable when meaning so firmly established or settled that change is almost impossible.
Inveterate applies especially to something which has persisted so long and so obstinately that it has become a fixed habit or an almost inalterable custom or tradition.
When applied to a person, the term implies the formation of a seemingly ineradicable habit, attitude, or way of acting or behaving.
Confirmed applies chiefly to something which has grown stronger or firmer with time until it resists all attack or assault or attempts to uproot it. Like inveterate, it may also apply to a person who is such as he is described in the noun by the strengthening or crystallization of a taste, a vice or virtue, or an attitude.
Chronic also implies long duration, but it applies either to diseases, habits, or conditions which persist without marked interruption in spite of attempts to alleviate or to cure them or to the persons who are afflicted or affected by such diseases, habits, or conditions.
Deep-seated and deep-rooted in their extended senses emphasize rather the extent to which something has entered into the structure or texture of the thing (as a person’s body or mind or a people’s nature) in which it becomes fixed or embedded.