Authoritarians seems to rise when basic national and cultural health is seen as greatly suffering and the powers that be are doing nothing about it or are even encouraging the destruction. The authoritarian and his fellow travelers see this happening and decide to do something about it, that is, the authoritarian says he knows what the nation and culture need and he does not want to merely give the people what think they need, as demagogues might do.
The authoritarian thinks that the powers that be are not mending the dying culture but making it worse. But why would people want to make the culture worse rather than better? The perpetuaters of the destruction often gain personal power for themselves or their groups by destroying or nearly destroying everyone else. The authoritarian usually thinks that democracy is too slow and is too easily manipulated or exploited, and so no improvements are happening with democracy.
So if the authoritarian---or the advocate of democratic republics for that matter---are politically and culturally healthy they will not say they are going to "make it new" but say that they will "make it better." Change is best made within conservative traditions that follow basic human nature, which is conservative.
As I say here often, the least we should do is reaffirm our original democratic republic, where ultimate power rests in citizens who are entitled to vote to elect representatives to wield that power, whereas in direct democracies, which we have drifted into, people vote on policy directly. Democratic republics are probably as close as we can come in the modern world to aristocracies, that is, rule by the best, ideally chosen from merit.
Then we can work on creating an ethnopluralism of ethnostates in America, more in line with real kin-centered and ethnocentric human nature, which the Founders didn't anticipate, not foreseeing the now violent competitions between distinctly different ethnic groups within the nation. All this can be done conservatively and legally by affirming, but adapting, the constitutional separation of powers and states.
Otherwise democracy will fade simply because it no longer works, and the natural need for order which is required to live healthy lives could choose authoritarian undemocratic Marxism, or fascism.