What is Ad Vitam Aut Culpam?

Legal Definition
Ad vitam aut culpam is a Latin phrase found in Scots law which meaning "for life or until fault" which guarantees the right of a Sheriff Depute (judge) to hold office permanently or until they forfeit such by misconduct. The Heritable Jurisdictions (Scotland) Act 1746 used the phrase to guarantee a Sheriff's term office after they have held office for seven years.

The applicability of this law was decided upon by the House of Lords in the case Stewart v. Secretary of State For Scotland where it was stated this it did not protect a Sheriff from dismissal for inability. Further Acts of Parliament empowered the Lord President of the Court of Session and the Lord Justice Clerk to remove Sheriffs from office due to a personal inability to complete their function – differentiated from a mental incapacity or incapacity due to age. Therefore, ad vitam aut culpum has a limited applicability which does protect an office from dismissal if they are incompetent.
-- Wikipedia
Legal Definition
An office to be so held as to determine only by the death or delinquency of the possessor; in other words it is held quam diu se benegesserit.
-- Bouviers Law Dictionary
Legal Definition
For life or until fault. This phrase describes the tenure of an office which is otherwise said to be held "for life or during good behavior." It is equivalent to quamdiu bene se gesserit
-- Black's Law Dictionary
Legal Definition
For or during good behavior.
-- Ballentine's Law Dictionary