I offer the case of a country where a movement became active to give women the vote in 1919, even before implementation of the 19th Amendment in the US ensured suffrage for the women there: Afghanistan.
Yes, Afghanistan. Who would think of THAT country as being ahead of the United States in the area of women's rights? Yet, in the 1920's, it was--at least on paper, and at least in the media. But it was a top-down revolution, and, as these tend to do, it didn't last.
In 1913, Emir Amanullah Khan took Soraya Tarzi as his third wife, having divorced the first as a teenager and losing the second to death in childbirth. But, unlike every monarch throughout history to precede him on that throne--he himself being the son of his predecessor's second wife--he announced that as of Soraya, he was done taking wives; the Christian notion of monogamy seemed, to him, something that his Islamic nation could adopt to their betterment. Emir Khan proclaimed himself King in 1919, ousted the British Overlords in the Third Anglo-Afghan War, and as the decade of the Roaring Twenties dawned, set about to bring his country into the 20th century--starting by elevating women to a status equal with men. This move, which included appointing his wife as Minister of Education and opening that world to the female half of society, was directly contrary to the teachings of Islam. The Qur'an states, in An-Nisa 4:34,
"Men are in charge of women, because Allah hath made the one of them to excel the other, and because they spend of their property. So good women are obedient, guarding in secret that which Allah has guarded. As for those from whom ye fear rebellion, admonish them and banish them to beds apart, and scourge them. But if they return to obedience, seek not a way against them. Surely Allah is higher, great."
This top-down revolution was thus doomed from the moment it began, and by the close of the decade Amanullah and Soraya were in exile, never to return home until their respective royal burials in the 1960's. Amanullah couldn't even manage to keep of the reforms in his personal life; although he held on to Soraya and went on to father ten children through her, he lapsed back into polygamy by briefly marrying his first cousin in the dying days of his kingdom.
The remainder of the century would see Afghanistan endure one government overthrow after another, with women in he forefront politically whenever they were permitted it, and then thrown back under the bus when Islamic doctrine prevailed over Western thought.
So here is what it comes down to: whenever modern doctrines like the equality of women hold sway over the ruling class, women get the vote; but whenever the core beliefs of the nation at large gain the preeminence, women lose it again. This process has repeated itself in Afghanistan probably more times than in any other country, but it serves as an example of how it could happen anywhere else. In the USA, the process is still on its first cycle at the national level--but it we were to peer closely down to the local level, we would see that the second cycle has already begun to play out.
I can now envision a movement in which women are taught that their inherent status is one of submission to men, and where they either give up the vote altogether, or only vote as their husbands instruct them. This would be the most peaceful option, in which the female vote is surrendered voluntarily. But should that option fail, men could still win back exclusive suffrage by brute force, womankind being much less of a match for mankind militarily, as they are politically.
And in a nation whose women only ever vote in accordance with their husbands' wishes, there is actually no need to abolish female suffrage, in order to obtain an equivalent result.
