Yeah, modern dictators aren't what I would call "popular". They have a sort of fake/forced popularity but their population generally fucking hates them. It's just force that keeps them popular.
Most despots, historically and today, have a power-base. They have sizeable segments of the population that they keep happy. Iran would be an obvious example - we keep hearing how people are "tired of the regime", but there's clearly a significant demographic that still mostly supports them (I'm guessing, much as with the US, it's mostly rural, uneducated, and religious).
The despotism part just means it doesn't have to constitute a numerical majority, but regimes still need a degree of popular support.
[Edit] Actually, with Iran I suspect it's possible they might get tired of the religious conservatism, but any replacement regime will probably embrace aggressive nationalism even more than the current regime, and be even more anti-Western, anti-US, and anti-Israel.