Elected and then keeps the office for four years? You're still denying the people their right for 3 years, 11 months and 29 days.
I don't think that any system of government should only consult with the people on election day.
Regardless, I'd say that if there are signs that the people have had a strong change of heart since the last election, elected officials are duty-bound to take this into account (such as by dissolving Parliament and holding a new election).
When you elect a monarch for life, you not only have the problem that people can sometimes change their minds; you're also dealing with a largely different group of people. After, say, 20 or 30 years, the electorate will include many people who weren't of voting age (or maybe weren't even born) when the king was elected.
And what about constitutional monarchies like in the UK, the Netherlands, Denmark, Belgium etc?
They're something less than full democracies, and all deny the rights of their citizens to some degree. How much they do this depends on the specifics of each country's system.
No, I think it is useful to keep to the principle that only actions can be (im)moral.
I never said anything different. My point is that a monarchy isn't a monarchy unless certain actions happen... i.e. denial in some form of the right of the people to choose their government.
I'm saying that the actions that are necessary for a monarchy to exist and perpetuate itself are immoral.