Ultimately, even democracies need a good old-fashioned dictator from time to time to get things done. This is in essence the rationale behind the declarations of State of Emergency by certain governments; what they're saying is that while the emergency is happening, voting is suspended, the constitution is suspended, and everyone has to do what the leader says.
In practice in most democracies, this is used to marshal responses to cyclones (or typhoons, hurricanes or tornadoes depending on your region), tsunamis, volcano eruptions or other natural disasters. Generally, nothing is really done that would violate the constitution anyway, and when all is back under control the state of emergency is lifted.
That said, many of the countries affected by the 'Arab Spring' had States of Emergency in force for around 30 years, with the leaders clinging to power via that method. So, it can be abused.
Imagine a nation where they're faced with constant threats; war, famine, natural disaster. Maslow's Hierarchy of Needs dictates that the populace just want to survive. Their sense of significance (represented by their ability to vote) is no longer as important to them as that sense of security they get from a competent government managing armies, food supplies, disaster relief, etc.
In such a case, a long term benevolent leader who has proven to be fair and competent in distribution of vital supplies, dealing with insurgents, etc. may be seen as a viable 'permanent' alternative to constantly having to vote for someone who says one thing to get voted in and then always does something else. Reliability and trust comes into play here and it may well be that electing someone like our 'hero' on a permanent basis means the populace can focus on the day to day of their lives, and leave the strategic planning with someone they can trust.
What history has taught us though is that the competence of the father is not always visited upon the son. (Not saying this selection should be along gender lines, this is just a figure of speech.) In that sense, I suspect that instead of a traditional hereditary monarchy, you'd have a council select a new leader for a lifetime appointment upon the death of the last king or queen. Kind of like a supreme court judge appointment in the USA; selection based on competency and the council then reverts back to executing the orders of the new monarch and in time sets about succession planning when the time is appropriate.