When you lose elections, must you back down?

I think the reason why they do it is because they calculate that a dose of humility will help them to win back voters.

But you are correct that people are still free to advocate for their beliefs even if they have suffered a defeat at the polls.

Yes, it's social logic either way. In social logic, there is no pursuit of right/good outside of what social consensus supports. A person doing the right thing or seeking to do the right thing has no legitimacy in minds of social-oriented morality, unless they are supported by others.

Likewise, a person or party that has no inherent legitimacy can be legitimated by social/political support in social logic. E.g. Hitler's Nazi party was elected by majority referendum, and they might understand on some level that that's wrong, but they think that there is no recourse without gaining popular/social support.

What I see is that goodness gets squelched by evil and the oppression keeps growing until it begins to generate madness and violent eruptions in societies, and then more insanity is generated to deal with the madness and violence. Within that soup of negativity, some clarity of vision emerges here and there, but gets squelched by popular conformity to ideas and beliefs that are inherently biased against reform.

Still, it is the job of those who see things clearly to go on pursuing their POV despite losing elections or any other obstruction that comes. Goodness is always a small search light within a vast darkness, but you have to go on shining that light regardless of unpopularity, because doing so encourages others to do the same instead of giving into majoritarian/popular madness.