Árni made a late marriage in 1709 to Mette Jensdatter Fischer, widow of the royal saddlemaker, who was 19 years older and wealthy. He returned to Iceland only a few months later to continue his work on the land register; they corresponded by letter until his return to Copenhagen. He lived only a little more than a year after the Copenhagen fire, dependent on friends for lodgings and having to move three times; the winter was harsh and when he fell ill, he had to have assistance to sign his will. He died early the next day, January 7, 1730, and was buried in the north choir of the still-ruined Vor Frue Kirke. His wife died in September and was buried beside him.