You've diagnosed the problem, but misdiagnosed the solution. The insurgency continued for four years in Iraq because the Sunni-Arabs were convinced that if they hung on long enough that could outlast us and then go to town on the Shiites. They have finally been disabused of that notion by the tenacity of President Bush our troops and, more importantly by, what the Shiites did to them after the bombing of the Golden Mosque in Samarra. In effect, the Shiites undertooks sectarian cleansing of large parts of Baghdad in 2006. They beat the Sunnis and their proxy, Al Qaeda, in the battle for Baghdad. That is what finally convinced the Sunni-Arabs that the insurgency was a loser.
One example of this change in mindset can be found in recent made comments made by the leader of the Sunni Religious Endowments, Sheikh Ahmed Abdul Ghafour al Samarrai, who criticized the Association of Muslim Scholars for directing Sunnis in 2005 not to join the American-backed Iraqi Army and local police forces
The Association has been an obstacle in the way of entry of our sons (Sunnis) into the ranks of the Army and the police. ... [In] April 2005 more [than] 60 Iraqi clerics gathered and we published a fatwa (in favor of) joining the ranks of the Army and the police.
The Association's leaders announced on the television screens that the Association disavows this fatwa, and they took into account members of the Association who issued the fatwa with us. Because of this, tens of thousands of our people have been reluctant to volunteer in the ranks of the Army and the police. ... [This decision] upset the balance [and led to a] catastrophe.
As Samarrai notes, the failure to join the Army and police forces is was a catastrophe for the Sunnis, because it gave the Shiites a free hand to use the Army and polices forces to cleanse Baghdad of Sunni influence.
With most of America screaming for troop withdrawl, I am not yet convinced that sectors of rebelious Sunnis aren’t intentionally reducing their number of attacks until we do withdraw. Then they will have an almost unresisted freedom to slaughter the Shiites with their homemade cheap, but seriously effective IEDs knowing that our Congress will never permit a return of our troops.