Far be it for me to judge now, but it seems like the Court at Vienna fell for every trap set for it from 1849 on. What if they handled things more nimbly starting with the Hungarian War of Independence, The Punctation of Olmutz, The Crimean War, The Italian conflict or German Unification? Everyone knows Austria loses wars, so why not pursue advantageous compromises?
1849: Austria-Hungary created early on terms more favorable to Vienna (for example generous autonomy packages for Croatia and Transylvania and an enlightened Nationalities Law). Obviates reliance on Russia and consequent embarassment. Reconquer Lombardy-Venetia, but spin it off as a saellite Kingdom under Ferdinand Max.
1850: Austria offers Prussia enticing alternatives to the Erfurt Union. How about the 1815 Bund is restored but Prussia assumes military administration of North Germany? In return, Prussia allows the merger of the Zollverein with the Austro-Hungarian Customs Union. I think the Prussians would fall for this and not realize their error until it was too late. Austria will achieve its goal of a large Cental European trading area centered on Vienna.
1853: Flatter Napoleon III. Recognize his empire and procure a nice Bavarian bride for him. Helene in Bavaria? Franz Joseph and Napoleon III could be brothers-in-law.
1854: United action by Britain, France and Austria deters Russian moves in the Balkans. The French decline to join Britain in chasing the Russians to the Crimea so that War does not occur. Instead, Austria allows regime change in Naples...the Bourbons are replaced with the Bonapartes. In return France spurns Sardinian overtures.
1857: Russia again rattles her sabre in the Balkans as Britain is busy with the Sepoy Mutiny. A Quadruple Alliance of Britain, France, Austria and Turkey deters this move. Frustrated in Europe, Russia expands into Central Asia. The Great game begins.
SO far so good? This game plan put Austria in a better position internally as well as in Germany and Italy. She is also a sought after ally in this scenario.