Stipulate the following: a boycott designed around primarily economic ends--attempting to deny to a company or organization a sufficiently large amount of money that it would contribute in a notable way to the company's inability to continue in the future--is destined to fail. For almost any company, it will be difficult to organize enough people to make an economic impact, and to keep them committed for long enough to make that impact felt. The difficulty in organizing anything so simple as a one-day boycott (see for example the endless waves of "gas price protest" emails that went around in the late 90s) should make this clear.
The purely economic boycott fails for another reason, though: it is, and only can be, a purely negative, punitive act. The point of the economic boycott is to punish. This fact has consequences for the public perception and inner constitution of the people engaging in the boycott. Public defenses of the boycott too easily slide into the realm of the vindictive, making it difficult to engage more members of the public and encouraging punitive counter-protests. Similarly, the desire to boycott is coterminous with the desire to punish: thankfully, most human beings lack the ability or interest in punishing someone else for an extended period of time. If you rely on hate, however deserved and however attenuated, that becomes a hard burden to carry.
Counter-thesis: successful boycotts aim at moral, rather than economic, ends. The idea behind a moral boycott is this: that the people involved would rather do great inconvenience to themselves than accept unjust or unfair treatment from the persons being boycotted. Thus the Montgomery bus boycotts: the point was not to bring down the system in a purely economic sense, which would have been difficult or impossible, but to show in the willingness to personally take on hardship, difficulty, and inconvenience, the injustice of the system they oppose. The attitude is internally focused: rather than hating the people perpetuating the injustice and punishing them, the boycotters direct that urge inward and make their suffering the sign of their cause. It is this that grabs attention: nothing is more confusing to an American than someone making their life more difficult when it might be easier--nothing is more certain to force our attention. So also for the divestment movement in South Africa: a capitalist company that forgoes profits becomes a powerful signal.