What was unsuccessful about dynamic conservatism?
Eisenhower's "dynamic conservatism," at least in his mind, was supposed to combine fiscal accountability and limits on the power of the federal government with a humanitarian concern for the American people. In many ways, this meant accepting, albeit in a limited sense, some of the basic ideas behind the New Deal of the 1930s, basically that the federal government had a role to play in bettering the lives of its citizens. Eisenhower was by nature conservative and, while president, he opposed federal subsidies for education, a federal healthcare system, and other liberal causes that even many Republicans at the time favored. But he also generally (if not enthusiastically) supported organized labor and opposed, for political and ideological reasons, cuts to Social Security and other social legislation that had become mostly accepted by Americans, if not the hard right. In fact, many of Eisenhower's political adversaries were on the right, and this was the reason that he failed to pass much of his agenda. Many urgent social problems went unaddressed moving into the 1960s, especially the conditions confronted urban populations left behind by the "white flight" to the suburbs.
As for specific failings of this brand of conservatism, it could certainly be argued that Eisenhower's reluctance to involve the federal government in implementing the Supreme Court's decision in Brown v. Board of Education enabled what came to be known as "massive resistance." As one historian has said, "Anti-Brown agitators took...heart from the attitude of President Eisenhower," who while somewhat personally sympathetic to the plight of African-Americans, was "dead-set against using the federal government to force the South to mend its ways." His "morally obtuse" position on Brown and integration in general encouraged Southerners (most visibly Orval Faubus of Arkansas) to oppose its implementation. Of course, Eisenhower eventually used federal troops to force integration of Little Rock Central High, but overall his limited view of the powers of the federal government afforded very little support for civil rights activists.