The Iranian constitution gives the Assembly of Experts explicit power to select the next Supreme Leader if he dies. However, they are also required to meet 2 days out of very 6 months, which seems rather frequent given how rarely they have to exercise their constitutional power. What I'm not sure about is why exactly the Assembly of Experts has to meet so frequently, and what they do during their meetings.
The point is in your statement: "select the next Supreme Leader if he dies." The Leader is not selected for lifetime; He must have and preserve qualifications and conditions (articles 5 and 109) to remain leader. Assembly of Experts have supervision duty, to check if the Leader qualifies and preserves these conditions; If not he will be dismissed.
Whenever the Leader becomes incapable of fulfilling his constitutional duties, lacks one of the qualifications mentioned in Articles 5 and 109, or it becomes known that he did not possess some of the qualifications initially, he will be dismissed.
The authority to determine this matter is vested with the experts specified in Article 108. In the event of the death, resignation, or dismissal of the Leader, the experts shall take steps within the shortest possible time for the appointment of the new Leader.
Also Assembly of Experts Legislate for Assembly affairs.