Military force is one of the oldest tools States have been able to wield. Dating back to antiquity we have records that even the earliest civilisations have used the idea of organised violence to achieve their aims, both domestically and beyond their borders. This has been a fairly consistent theme throughout recorded history, from feudal kings with knights and liverymen, to the conscripted Grande Armee of Napoleonic France. However, over the last century the international system has changed, with the creation of regional power blocs and the development of soft power. When this is coupled with the creation of nuclear weapons and mutually assured destruction, diplomacy rather than war has been preferred.
Why has this occured? When did Military Intervention fall out of favour?
First, I'm not sure I agree with your premise. There have been many military interventions in the post-WWII period. If anything, the number of military activities has likely increased from the pre-WWII period. The character of these may have changed: what one sees are less large-scale conflicts between industrialized nations, and many small-scale civil wars, proxy wars, and "insurgencies." Many of these involved larger states albeit in more reduced roles. It is true that the death toll of these is lower both in raw numbers than the earlier period (if only because a few of the earlier wars, like World War II itself, had such monstrous numbers of casualties) and in terms of deaths per capita (which is partially a function of the fact that the global population grew exponentially over this period, diluting almost any effect per capita), but it is still quite a lot of conflict. If anything I suspect that if one added it up, one would find far more wars in the post-1945 period than one would find in any other 75 year period in history, enabled by a context of free-flowing resources from superpowers, as well as volatile ideologies, new logistics (so that Chinese-made AK-47s can easily make their way to other continents), and rapid communications. There are several major wars going on as we speak (e.g., Afghanistan, Yemen, Syria) and many minor ones (e.g. Ukraine, Iraq, Libya).
Now, if one wants to ignore all of the "small" wars (some of which had fatality rates in the millions, but whatever), and ask, why has great power conflict changed? — I mean, you sort of answer that yourself. The cost of great power conflict has increased. Not just because of nuclear weapons — though those certainly raise the stakes. But World War II, even without the nukes, was devastatingly bloody and is not exactly something that anyone has been desperate to repeat. The nature of technologically-driven war had gotten unsustainable on such scales as one finds between two fully-industrialized nations. Nuclear weapons raise the stakes ever so much higher, allowing — at the worst — total annihilation of nations within hours. This is not to say that deterrence cannot fail or that everyone involved has been logical, but these conditions have created an impediment for anyone wanting to engage in large-scale war: the potential consequences would be catastrophic. And so the recourse for states expressing their power claims has been in diplomacy, economic warfare, and, as mentioned, lower-level war by proxy.
The creation of the United Nations was intended to create avenues for countries to prosecute their grievances short of military action. It has hardly been perfect in that respect, but it is part of the overall post-WWII approach as well.