Been researching this topic and finding it hard to find any explanation other than there was a successful balance of power.
The Long Peace is associated with Pax Britannica. There were several conflicts that threatened to change the balance of power in Europe. The Unification of Germany and Italy, the Austro-Prussian and Franco-Prussian wars changed the dynamic in the Concert of Vienna. We know that the European monarchs were facing several reformist, nationalist movements, and revolutions such as the that occurred in 1848 across continental Europe. There is also the Crimean War where several European powers were frightened over the decline of the Ottoman Empire and Russia's willingness to fill the power vacuum in the Eastern Mediterranean.
The period is highlighted with social and political movements inside every nation when they were run by reactionaries and the end of the Napoleonic Wars led to people such as Metternich of Austria, Talleyrand in France, Tsar Alexander I, and Castlereagh to promote the 'balance of power' ideals and attempt, as realistic as possible, maintain the status quo as long as possible to avoid another great war.
Add-on question for whoever can answer the main question:
I've never heard of it before, but some Googling seems to confirm that this "long peace" idea is (or was) a thing. No doubt it is an idea which past historians could have supported, considering the development of the profession. I'd love to hear more about the historiography surrounding it. What is the history of this idea? When did it get started? When did get buried? (Please tell me it's been buried by now.)
edit: spelling