The continued importance of single-sex education

The recent near-closure of Sweet Briar, an all-women's college in Virginia, has rekindled the debate over the continuing relevance of single-sex education.
Single-sex education has a long history, because for millennia many institutions of higher learning refused to admit women; Plato's Academy in fifth-century Greece was all-male (ok, two women were allowed to study there), and so was Dartmouth, my alma mater, until 1972.