They ran them, and even though most of those women may have been republican, they were "real" debates, and had strict rules. Of course they were as exciting as watching paint dry, so they were eventually wrested away from the LGWV..
http://en.wikipedia.org/wiki/United_States_presidential_election_debates Debate sponsorship
Control of the presidential debates has been a ground of struggle for more than two decades. The role was filled by the nonpartisan League of Women Voters (LWV) civic organization in 1976, 1980 and 1984. In 1987, the LWV withdrew from debate sponsorship, in protest of the major party candidates attempting to dictate nearly every aspect of how the debates were conducted. On October 2, 1988, the LWV's 14 trustees voted unanimously to pull out of the debates, and on October 3 they issued a dramatic press release:
The League of Women Voters is withdrawing sponsorship of the presidential debates...because the demands of the two campaign organizations would perpetrate a fraud on the American voter. It has become clear to us that the candidates' organizations aim to add debates to their list of campaign-trail charades devoid of substance, spontaneity and answers to tough questions. The League has no intention of becoming an accessory to the hoodwinking of the American public.
The same year the two major political parties assumed control of organizing presidential debates through the Commission on Presidential Debates (CPD). The commission has been headed since its inception by former chairs of the Democratic National Committee and Republican National Committee.
Some have criticized the exclusion of third party and independent candidates as well as the parallel interview format as a minimum of getting 15% in opinion polls is required to be invited. In 2004, the Citizens' Debate Commission (CDC) was formed with the stated mission of returning control of the debates to an independent nonpartisan body rather than a bipartisan