Here's my understanding of what has happened.
In January, after Flores testified, the Defense filed a motion to dismiss the death penalty as an option because of the conflicting testimony about the aggravating factor. The trial judge denied their motion, and the trial continued.
The defense then filed a special action to review the judge's ruling on the motion to dismiss the death penalty. This was filed with the Court of Appeals in January, and at the same time they filed a "motion to stay", which is a request that the trial be stayed or postponed until after a ruling on the special action. The Court of Appeals denied both the special action and the motion to stay.
Today, the Defense then field the same special action and another motion to stay with the AZ Supreme Court (kind of like an appeal of the Court of Appeals ruling denying the special action). The AZ Supreme Court has denied the Motion to Stay, so the trial will continue - and I'm not sure whether the court has ruled on the special action requesting that the death penalty be dismissed.