Gay rights has made stunning progress in the last decade, but the same is definitely not true for the pro-choice movement, who are losing ground and suffer setback after setback. I don't think the GOP is losing the abortion debate at all.
The right lost the debate when the Supreme Court ruled on Roe v Wade. There cannot be a federal blanket ban on abortion. The only people that talk about it are people fishing for votes from idiots.
Individual states pass some antiabortion laws when Republicans are in power but they are only shooting themselves in the foot. The wealthy and middle class can afford the $500 for an airplane ticket and hotel to get an abortion in a more civilized state. The Red states are then stuck with poor women ballooning their welfare rolls and restocking their prisons. If you call that winning I don't know what to say.