Throughout the 19th century, Austria's major national minorities -- the Magyars, Italians, Czechs, Croats and Serbs -- all posed a problem to Austrian power and empirical stability. The ruling class was challenged again and again; each time making concessions to stay in power until they were diminished. Their greatest threat was the same one that threatened them every time: nationalism. It took different forms, such as the 1848 revolutions, the liberalism of the February Patent, and the Pan-Slav Congress; they were all nationalistic minorities trying to grab power and break away from the Austrian Empire.
The Magyars, in the Hungarian portion of the Empire, caused a good deal of trouble in their nationalistic struggle. After the 1848 revolutions all around the Austrian Empire, the Bach System, named for Alexander Bach, the Austrian minister who created it, was established. Even though it didn't really encourage Germanization, that was one of its results, as it dismanted Hungary into five "governments", and destroyed its historical identity. Bach centralized the growing bureaucracy, and for over ten years, until 1859 this repressive reaction was in place.
Francis Joseph's October Diploma and February Patent, documents that created local diets and centralized legislation respectively, was yet another response to the growing nationalism, trying to keep them a part of the Austrian Empire. And ultimately, the Dual Monarchy, the Ausgleich with the Hungarians, gave up ultimate control of the throne from the Austrians, also creating the Delegations, a legislative system that gave the Hungarians a large say.
A general pattern here is appeasement -- what the Austrians really want is a return to the Holy Roman Empire; but Emperor Francis Joseph knew that when it came to nationalistic minorities in his own country, they had to be unified in order to expand back to the glory of ages past. However, they weren't unified, because all the minorities wanted their own countries: Hungary, Yugoslavia, Italy, and so on. So in order to keep them in the Austrian Empire, the decadent government continually threw them bones. Their response of appeasing the minorities -- effectually compromising with them (actually, Ausgleich means compromise) and giving them some of what they wanted to shut up for a while.
Things like that can't go on forever; eventually you give them everything (which of course, is what they wanted). Near the end, that's pretty much what the Hungarians had, with the dual monarchy and the delegates. But the Austrians couldn't do this with all their minorities; otherwise they'd end up with a Quadruple Monarchy (or something like that), which would be less than ideal. Even a Dual Monarchy, the way it was set up with an Austrian on the throne but basically everything was split in half. The problem was though, that the Magyars weren't the only ethnic group in Austria; and those minorities didn't have independence. While the Dual Monarchy required a Catholic on the throne, what about those ethnic groups that were Muslim or Eastern Orthodox? They were left out of the loop.
It was these sorts of problems that plagued the Austrian response to nationalism, that of ignoring certain ethnic groups and acknowledging others, that lead to revolts in Bohemia and Italy, and ultimately this lead to the decline of Austria and the rise of Prussia (Klein Deutsche) because Austria had to deal with their internal problems (nationalism) before they could really focus on international relations and growth.