Shortly after the fire Qatar police held four Villaggio mall management officials and Iman Al Kuwari, the Qatari owner of Gympanzee, for questioning.
Villaggio has been closed since the fire.
Earlier this month the court case to determine who was responsible for the fire was postponed because two of three parties charged did not turn up to court.
Representatives of the Villaggio Mall attended the hearing, but no one from the Municipality and Gympanzee were there, prompting the hearing to be postponed until next month.
An initial report, completed in June, found negligence by many parties led to the blaze.
The Wellington parents of the triplets, Martin and Jane Weekes, last month called for a boycott of the Villaggio shopping complex until their concerns were dealt with.
They joined the parents of the other children killed - from eight different countries - in sending an open letter to the Doha News newspaper.
"To the editor, It is outrageous, hurtful and indefensible that the owners of Villaggio Mall would celebrate the reopening of the place where our 13 children died, especially given that we have not heard a thing about the investigation, have not been apprised of any meaningful reforms in the wake of the tragedy, nor received an offers of a just financial settlement."