Answer:
The Austrian-Hungarian Empire, which rose after a long struggle from what used to be the Holy Roman Empire, the defeats against Napoleon and the loss of territories and authority in the early 1800´s, became a powerful and extensive empire after the Congress of Vienna, where, thanks to efforts from different fronts, Austria received benefits, among which, were lands.
At the accession to the throne of Francis Ferdinand, in the late 1800´s, after several separatist revolutions, nationalist movements and pressure, the emperor was able to maintain his hold thanks to his efforts to negotiate with these separatist movements, and also make arrangements with his international oppressors, especially Russia, Prussia and France. This, he did, by joining the Kingdom of Hungary and the Empire of Austria, to form the Austro-Hungarian Empire. The problems, then, lie here, and this led to the dissolution of the Empire itself:
First, with the annexation of Hungary as as an equal party to the Empire, the power of the Emperor was divided into two very different lands, with very different cultures and traditions. This meant that the concentration of power was less. This made it more difficult for the Empire to defeat its internal opponents, which were many, especially separatist movements.
The second were a series of wars with foreign kingdoms, particularly with Prussia, and with others, that undermined the power of the Austro-Hungarian Empire.
But the final event that led to the break of the Empire, was the assassination of the heir to the throne, and the initiation of the First World War, when Austria became entangled and was finally defeated and broken up.