Any government that lacks public support collapses.

Democratic governments can operate without a plurality of support for the current government, because the population generally supports and is invested in the system of government. When democratic governments fail, there is usually very little danger of violence or economic and societal instability, because there is trust in those systems. Corruption and malfeasance harms trust in the systems of governance which democracies depend upon.

Authoritarian governments depend on confidence in the government to continue functioning. The system of government isn't necessarily trusted, the workers of government aren't necessarily trusted, but the leaders are in charge and doing things. Media manipulation and effective propaganda is certainly an important tool for these governments, but pointing out that it exists doesn't mean that it doesn't work! Propaganda totally does work, by almost all measures. Russia, China, Cuba, Iran all have high domestic support for the government.

Authoritarian governments also tend to be very stable - people know what to expect. Democracies change periodically. The stability and familiarity are key to the trust that authoritarian governments maintain. The protests in Iran prior to the current conflict are a good example of what happens when a government fails to maintain the trust of the people - the arrival of war saved the current regime from falling apart at the seams when Khomeini died of cancer in a few months and a squabble for the leadership broke out amid a collapsing economy.

I think that you're underestimating the power of authoritarianism. For Iran, I don't think the government was in any danger prior to the war. It was capable of exerting control through the state apparatus quite easily. And look at North Korea, you think that the people under that government are supportive? That's nonsense on stilts.

Also, that collapse you refer to can take an awful long time under authoritarian control.