Eric Gould, Omer Moav and Avi Simhon offer a new answer in the March 2008 American Economic Review: female inequality. Economic growth means that some women have higher human capital than others and thus they are better suited at producing and rearing high quality children. Wealthy men with lots of human capital will start to bid for these women and they will have to offer them exclusive status; these men also wish to invest in a smaller number of higher quality children.
In other words, male inequality encourages polygamy while female inequality discourages it. Apparently female inequality has been winning that race.
The hypothesis also helps explain why polygamy unravels so decisively at some point. Since monogamy itself encourages children (including daughters) with higher human capital, initial tendencies toward monogamy are self-reinforcing.