The absolute majority requirement makes it extremely difficult for a third-party candidate to win the presidency because the individual states' electoral votes are allocated under a winner-take-all arrangement (with two exceptions).
Third parties often represent an ideology that is considered too radical by the mainstream parties and their constituents. They fail simply because the American political system is designed to support only two major parties. As well as this, 48 of the 50 states employ a winner-takes-all system for electoral votes.