Others say differently, From Wikipedia (caution, it's Wikipedia) [my bold below]:
The Department of Justice has taken the position in litigation that the Military Commissions Act of 2006 does not amount to a suspension of the writ of habeas corpus. The U.S. Court of Appeals for the D.C. Circuit agreed in a 2-1 decision,[48] on February 20, 2007,[49] which the U.S. Supreme Court initially declined to review. The U.S. Supreme Court then reversed its decision to deny review and took up the case in June 2007. In June 2008, the court ruled 5-4 that the act did suspend habeas and found it unconstitutional.[50]
Except for the fact that the Military Commissions Act of 2006 mentioned above applied to aliens rather than citizens, it was similar to the act under which Hamdi was denied habeas corpus as an enemy combatant by the Executive Branch of government. Here is what the 2006 act said:
Except as provided in section 1005 of the Detainee Treatment Act of 2005, no court, justice, or judge shall have jurisdiction to hear or consider an application for a writ of habeas corpus filed by or on behalf of an alien detained by the United States who has been determined by the United States to have been properly detained as an enemy combatant or is awaiting such determination." §1005(e)(1), 119 Stat. 2742.
But nobody is saying that the writ of habeas corpus had been suspended. In its arguements the government argued that Hamdi was not provided due process because as an enemy combatant he was not entitled to it, any more than any other prisoner of war was. They did not say he was not provided due process because habeas corpus had been suspended. Nobody in the Bush administration was claiming it was. None of the lower courts were claiming it was suspended.