Problem with restoring or creating a monarchy in a republic, is that too many people in the top government have too much to lose, compared to what can be won.
Ministers and presidents will be challenged on their position as well as their future prospects. Many politicians have an ambition of being president - i.e. are power hungry. With a monarch in place all those dreams are snuffed out.
Hence far more politicians will favor a republic if they see the posibility.
For many of the developed countries to revert to monarchism, it will take an event of serious concequences, such as massive popular uprisings, civil war or deep economic depression. If we look at the EU, that union itself will have to be dissolved and much turmoil will have to happen - a balkanization of sorts.
In that case, it's possible that several countries will see a strengthening of the monarchic wing - Germany, Italy, France, Portugal, Greece, Poland, Hungary, Romania, Bulgaria and most of the balkan countries.
But republicans will never volounterely yield power, even to constitutional monarchies, as it removes their chance of being "caliph instead of the caliph" (referenced from the comic iznogood).