I forgot to add in my other post, but basically the biggest danger isn't necessarily from the entire empire collapsing, but from the Hungarians deciding to leave. The Austro-Hungarian Compromise of 1867 gave Hungary sovereignty and was renegotiated every 10 years. Technically, the Hungarians could leave at one of the 10 year renegotiations. Unlike the secession clause in the Soviet Constitution, the Austrians and Hungarians were on equal enough terms that the Austrians couldn't just steamroll in to force the Hungarians back in. The Hungarians had their own army, and even if the Austrians succeeded they would face the daunting prospect of ruling the entire empire themselves. If the Austrians needed help ruling in 1867, it's certainly not going to be easier in 1907, 1917, 1927, 1937, etc.
To keep an Austro-Hungarian Empire, as opposed to Austrian and Hungarian empires, enough internal and external tension must exist to force the union without boiling over. Austria-Hungary probably has a better chance at reform (or at least staying together) if they still face major threats rather than if they are a major power. Why would Hungary want to lower its standing in the Empire if all their enemies are vanquished? They don't have to put up with the Austrians in that situation, they can go run their own nation and still command respect. They might even be able to command great power respect, since they would be politically important and militarily potent even by themselves. Anything in the Balkans would need Hungarian approval to happen, if not all of Southern Europe.