The military has dealt a decisive blow against al-Qaeda in Iraq but they are hesitant to claim victory since al-Qaeda has proved to be resilient and could continue attacking with limited forces:

The U.S. military believes it has dealt devastating and perhaps irreversible blows to al-Qaeda in Iraq in recent months, leading some generals to advocate a declaration of victory over the group, which the Bush administration has long described as the most lethal U.S. adversary in Iraq.
[…]
There is widespread agreement that AQI has suffered major blows over the past three months. Among the indicators cited is a sharp drop in suicide bombings, the group’s signature attack, from more than 60 in January to around 30 a month since July. Captures and interrogations of AQI leaders over the summer had what a senior military intelligence official called a “cascade effect,” leading to other killings and captures. The flow of foreign fighters through Syria into Iraq has also diminished, although officials are unsure of the reason and are concerned that the broader al-Qaeda network may be diverting new recruits to Afghanistan and elsewhere.
The deployment of more U.S. and Iraqi forces into AQI strongholds in Anbar province and the Baghdad area, as well as the recruitment of Sunni tribal fighters to combat AQI operatives in those locations, has helped to deprive the militants of a secure base of operations, U.S. military officials said. “They are less and less coordinated, more and more fragmented,” Lt. Gen. Raymond T. Odierno, the second-ranking U.S. commander in Iraq, said recently. Describing frayed support structures and supply lines, Odierno estimated that the group’s capabilities have been “degraded” by 60 to 70 percent since the beginning of the year.
Lt. Gen. Stanley McChrystal, head of the Joint Special Operations Command’s operations in Iraq, is the chief promoter of a victory declaration and believes that AQI has been all but eliminated, the military intelligence official said. But Adm. William J. Fallon, the chief of U.S. Central Command, which oversees Iraq and the rest of the Middle East, is urging restraint, the official said. The military intelligence official, like others interviewed for this report, spoke on the condition of anonymity about Iraq assessments and strategy.

In an honor based society, it might be beneficial to shame your enemy but declaring them defeated (though it could also motivate them to regroup and try again even if they are limited in resources).