Answer:
The following advantages of Absolute Monarchy are:
1) As the supreme head of the country, the King/Queen is the de facto richest person in the nation, rendering bribes and other forms of monetary corruption from businesses and agencies useless. (The head of a Republic is vulnerable to this).
2) Monarchs, serving their nation for life, seek long-term goals and are less likely to make decisions for short-term benefit followed by imminent disaster, such as overspending and other irresponsible actions whose consequences, in a republic, would be the next elected official's problem. Monarchs hence are more inclined to observe the possible long-term effects that may come back to harm them later in their lifetimes before they make a decision.
3) With only one ruler and no layers of government separating the people from their ruler, there is also a reduced, if at all existent, bureaucracy that would otherwise hamper policy implementation. The moment the king issues a decree is the moment the decree comes into effect. (In a republic, the bureaucracy is generally large and therefore slugish).
4) The King/Queen has historical and noble roots in the kingdom he/she defends, and hence, is a source of great national honor,pride, patriotism, and unity, all qualities and reasons for which the people look up to the monarch for guidance, strength, faith, leadership, and protection, especially in times of crisis.
It is the monarch's success or failure in fulfilling his/her duties for which he/she will be remembered for. It is hence a Monarch's best interest to do what is best for the country to insure that he/she leaves behind a powerful legacy.
5) The most poweful incentive for Monarchs not to compromise their people's rights and status as dignified citizens is the fear of revolution.
6) Much like private businessess offer the highest possible quality services to compete against other companies, Kings and Queens, out of their nation's sense of nationalism that is their very source of pride, also compete with other countries for the strongest economy to benefit their people and gain prestige above all other nations.
To be clear, these conditions are not always met, and this response is not an endorsement of monarchy, but rather reasons pertaining to theoretical advantages that can arise only as a result of strong and competent Monarchs.