Primarily, what happened was a major mistake on the part of the Solicitor General's office. The Supreme Court held that there was a "national consensus" against the use of the death penalty for child rape, and that said national consensus depended in large part on the absence of a federal law. But the capital punishment law for the military did already exist — everyone simply missed it until after the opinion was announced.
Louisiana seized on that oversight to ask for a rehearing. And now the Justice Department is backing that effort. While stating that it "regrets" not having brought the military law to the Court's attention, the government filing said that the decision "rests on an erroneous and materially incomplete assessment of the 'national consensus' concerning capital punishment for child rape. That error undermines the foundation for the Court's decision."
For Louisiana and the DOJ to get their rehearing, they have to get five votes from the Justices, with at least one of those votes coming from the majority in the original decision. Accordingly, it is unclear whether there will be a rehearing. If not, the reasoning in this case will remain flawed — fatally flawed — by the standards of many observers.