Luiz Fuentes, 33, appeared in a downtown L.A. courtroom Wednesday morning for a third arraignment attempt, but it was once again postponed.
Fuentes' attorneys insist their client has health problems. He appeared in court in a wheelchair.
The judge ordered Fuentes be held without bail until the new arraignment, set for Oct.7. He faces three murder counts in the deaths of his young sons.
The bodies of Luigi, Alex and Juan Fuentes were found in an SUV near Dolores Huerta Elementary School on Sept. 9.
If convicted, Fuentes faces the death penalty.