No society lasts forever. Sumeria, Egypt, Assyria, Babylon, Greece, Rome, China, the Ottomans, the Aztecs, the Mayans, Spain, France, Britain, and yes, even the United States, all had a chance to dominate the stage for a while. These empires flare up for a brief moment, setting the stage and the auditorium ablaze with light and color, and then they sputter and go out. It doesn't matter whether they oppress women, men, blacks, Jews, caucasians, or some other group, no society survives that long, and most empires fade from pre-eminence after just a few centuries. (As Nately realized in "Catch 22," America won't even last as long on the world scene as the common frog.)
What can last is a people's identity, and that also has nothing to do with whether they're a patriarchy. Israel's identity began with the Exodus, probably around 1,500 years B.C., and during the 3,500 years since then, its identity has survived oppression at the hands of the Philistines, the sundering of the kingdom under Rehoboam, the destruction of the Northern Kingdom at the hands of the Assyrians, the Babylonian diaspora and the destruction of the temple, the Hellenizing ways of the Seleucids, Roman conquest, the complete and total destruction of the Second Temple and a second diaspora that scattered the Jewish people all over the earth from the reign of Marcus Aurelius until 1948, as well as God alone knows how many holocausts, ethnic cleansings, ghettos, blood libels, and what else.
That record of survival has nothing to do with patriarchy. It has to do with a celebration that happens every year, when children ask their parents "How is this night different from all other nights?" and God's injunction to Jewish parents to teach their children the Law of Moses to their children every morning when they rise and every night when they go to bed. Every day the sense of Jewish identity is reinforced, and that has enabled the Jewish people to remain the Jewish people despite everything that has happened.
So if we worry about the survival of the American identity, take the time to learn America's story and pass it on to kids around you. My girls know the stories of Jesse James, Casey Jones, and John Henry; for that matter, even before they could read, they'd heard the stories of Éowyn at Pelennor Fields, of Henry Jeckyll and Edward Hyde, of Beowulf and Grendel, and dozens of other stories that matter to me. We've even told them about the Trail of Tears and the other tragic stories of the American Indians (not just the "safe" ones like Squanto, Pocahontas and Sacagewea), because that is part of their heritage as well.
If you're worried about the demise of America as a society, then I say you'd best resign yourself to it. All societies perish, especially patriarchies, because God casts down the oppressor and frees the captives.
If you're worried that America's not having enough children -- and don't kid yourself, the only reason our population has continued to grow is because we continue to attract immigrants -- then address your attention to what we can do as a country to make having children more practical and more feasible for families that want to have more kids but can't afford to. (Working to end our culture of consumption would be a good start.)