The risk increases as the woman gets older, but it's never zero. Also, when the woman is very young, there is a higher risk (though I can't find a good source for this in English). Most children with Down Syndrome are born to women below 35 years of age, because there are more pregnant women who are younger than 35 than older.

But this conspiracy theory is just misogynistic crap in my opinion. People should leave her family alone and have an opinion about her policies instead of making up stuff like this.