The answer to this open question is the following.
International support dropped so much in the second term of Bush's presidency due to many international affairs and the decisions Bush made to resolve them that affected the United States.
Domestically, Bush focused on the reformation of the social security system. But the focus of the international community was placed in Iraq. Bush's decisions in Iraq were questioned since the very beginning due to that he did not wait until the Security Council of the United Nations authorized military intervention. And when in there, nobody found weapons of mass destruction, the main reason for Bush to order the invasion.
During Bush's second term, the great recession hit, making the American economy very unstable. The unsteadiness of the economy stopped foreign investors from investing in American stock because they were uncertain if they would make their money back. For that reason, the international support of the United States dropped.
