People in the end want stability and order, and are sadly willing to make the terrible trade of exchanging their liberties and freedoms for the promise of order and security.
The best know example is the French Revolution, where after the overthrow of the Monarchy the country was wracked by constant conflicts as the Revolutionaries attempted to impose their order on France, but were constantly fighting factional battles amongst themselves, the monarchists and even the peasantry. After years of turmoil, the French were totally willing to overthrow the Revolutionaries in favour of "The Man on the White Horse"
The origin of the phrase
Other dictatorships have been imposed on populations throughout history, based on the promise of stability after a period of war or revolution. The Bolsheviks did this in Russia, the Italian Fascists and German National Socialists did this in the 1920's and 30's in Europe, Mao did this in China and the Taliban were initially welcomed into Afghanistan in the 1990's on the promise of ending the factional fighting between Mujahideen leaders who devolved into civil war after the defeat of the Soviet Union.
For your population, a return to the monarchy represents the best possible alternative to the current chaos and disorder. The King and Royal family may be buffoons, or even baboons, but this is still a much better situation than currently exists. You might note that the British put up with the Stuarts after the end of the Tudor line, despite the fact they were notoriously ineffective. Even after the English Civil War and the rule of Oliver Cromwell, Parliament was willing to welcome young Charles II to return to the throne, despite the very real risks this entailed. (Eventually the Parliament decided that the symbol of monarchy was what was really needed, and started hiring outside help to fill the throne).
The UK and United States represents outliers to the general rule, but they had or created strong institutions to provide the stability after the revolution was over, negating the need or desire to turn to a "Man on the White Horse" for stability.
So in your situation, monarchists will have a core of supporters who are willing to follow and serve the King out of a desire to re establish a stable royal order where they can conduct their business in peace and security.
Enough of this nonsense! Follow me as the King of Stack Exchange and live in peace and prosperity