The dear old holy Roman realm,
How does it hold together?
- Goethe, "Faust"
A moment of nostalgia
The fate of the late Holy Roman Empire was all but sealed in 1815:
While individual member states, such as Great Britain, were arguing for a re-establishment of the HRE by nullifying the (constitutionally dodgy) dissolution of 1806, the one person most resistant to the idea was emperor Francis II (I of Austria) himself; albeit a reactionary, he was unwilling to be emperor of traitors and turncoats.
Not that it would have mattered much at this point of time - the Holy Roman Empire had finally outlived its single remaining purpose during the Reichsdeputationshauptschluss, which abolished most of the tiny realms, and a renewed empire would not be any different from the German Confederation.
In a moment of nostalgia, the legacy of a millennium on his shoulders, he finally gives in to the idea and the Holy Roman Empire lives again. At least for a while.
Concert of Europe and Pre-May
The balance of power set up during the Congress of Vienna was enforced by the Concert of Europe, an informal, alliance of the five great powers (Austria, France, Great Britain, Prussia, and Russia), who met from time to time in congresses to deflate potential conflicts and ease tension in Europe.
The Concert of Europe was complemented by the Holy Alliance of Austria, Russia and Prussia, which aimed to keep the monarchies in power and the new ideas out of people's heads.
The Holy Alliance faltered during the May Revolutions of 1852, but the Concert of Europe endured, eventually leading to the establishment of the Everlasting Congress.
Revolution and War
The Carlist Wars, the Belgian War of Independence, and the Crimean War slowly but surely led to the May Revolutions of 1852, which toppled the Habsburg empire, saw a temporarily independent Poland, a united Italy, three different government systems in France in the span of two years, and the establishment of a "people's empire".
The forces of reaction were attempting to stop the revolutions, which once again started in Paris, from overthrowing the fragile order in Europe, but a levée en masse during spring 1853 enabled the people's empire to fight back effectively.
After the European Revolutionary Wars settled, the Empire stood unified and soon in an alliance of convenience with the Netherlands, the Polish remnant, and Hungary.