I had read that the Austro-Hungarian Empire's economy was actually increasing in the years up to World War 1, and the country was industrializing at a steady pace.
Correct. IIRC, Austria's economic growth was second to Russia in the period. While certainly lower, Austria did have a significant head start in the department.
I'm wondering if it's possible to keep Austria-Hungry around until World War 2 (or, in case World War 2 never happens, to around 1941). It can survive long after that if possible, but I want an AHE around at least until then.
Oh, and similar borders. It doesn't need to be wanked-out, but it can't turn to a shriveled husk either.
There's two options I can think of:
1. Austria-Hungary doesn't really reform, keeps staggering on through the years, kept intact by German intervention (originally, Germany didn't want too many Catholics in the Empire and the addition of the Austrian half of Austria-Hungary would allow them to establish an extremely powerful block). Eventually, a rational government comes to power in Germany and figures out that being shackled to a corpse is too much trouble, allows Austria-Hungary to finally collapse and annexes Austria, Bohemia and Kustenland.
2. Austria-Hungary does reform (what shape the reform would be depends, there were literally dozens of opinions at the time). Two variants were fairly popular among reformers at the time. Franz Ferdinand advocated a dictatorship from the centre via Imperial Decree (crushing Hungarian independence in the process) ... incidentally, he believed this to be necessary for some years before any increase in autonomy could be undertaken as doing it too early would only rip the Empire apart. The other idea was the opposite, increased decentralization which, unless handled properly, rip the Empire apart (there was, after all, no love lost between many of the nationalities in the Empire).
The first option is, basically, Germany maintaining the status quo until they get tired of it and simply let the whole rotten structure collapse. Status quo, as it was, was untenable without outside interference.
The second option would ensure internal stability (possibly, it depends on a number of factors, economic, social and cultural) ... pretty much without any end date.
This all, naturally, assumes a CP victory in the Great War. If this occurs before the War, it's likely that the internal chaos (caused by the groups that didn't get their way ... primarily Hungarians, possibly Czechs or Sudeten Germans) would trigger the Great War as every surrounding nation would attempt to get in on the game. The basic problem with any attempt to clean house in Austria-Hungary is to keep other nations from interfering (Italy, Romania and Serbia would certainly, Russia might to keep any chaos from spreading to it's own territories) ... basically an impossibility without a Great War or something to sufficiently distract other nations from foreign policy.
If the Central Powers lose the war, well, I won't say that it being ripped apart by the victors (and it's own nationalities) is inevitable ... merely very likely. It's possible, of course, IIRC, there was a proposal from Vienna regarding a separate peace with the Entente which, if accepted, would keep Austria-Hungary in one piece (OTL, it wasn't and was leaked to Germany, which quickly reined it's ally in for a fight to the end). Whether it would survive, however, would depend on the development of the war and the actions of the government. Would they go for reform? Certainly, most of the political groups were aware it was necessary (they just couldn't agree how).
I suppose I could add that there was another plan, turning a double into a triple monarchy. The proposed groups were either Czechs or South Slavs, but the plan faltered a fair bit when the people proposing it (Franz Ferdinand primarily, during his early years) wouldn't help the monarchy at all and would essentially give Vienna a second Hungary to deal with. I suppose, if you want Austria-Hungary to last only a limited amount of time (say, to 1940 or so), you could have them go for the triple monarchy plan (or even quadruple monarchy by adding both South Slavs and Czechs as separate groups). It'd probably stagger on for awhile before collapsing.