Wouldn't a proactive ruler just have brought disaster in the short term?
Looking at Franz Ferdinand's plans for the monarchy (the dictatorship from the cente circa 1914 rather than federation idea from earlier)? Probably. The man's wish to ally with Russia and emulate the autocratic emperors would make things even worse - especially given his open enmity with the Hungarian aristocracy (I could honestly see Franz Ferdinand launch War Plan U and start a civil war with Hungary). So, avoiding WWI ... Austria could survive, but if it did, it would survive in spite of Franz Ferdinand rather than because of him, though Sophie might be a moderating influence.
Karl I/IV had some more reasonable ideas driven, in large part, by desperation and an awareness of the Empire's weakness. The seperate peace was basically the last reasonable chance to salvage anything.
Fundamentally, the Empire made a few crucial mistakes early on (as in pre-1848 early), which would be difficult to fix. Not impossible, but difficult - made even more difficult by the presence of countries with ambitions on Austria's borders (Russia, Italy, Romania and Serbia would all happily stab Austria to neuter a rival/get their rightful territories). By 1914, it was widely believed that something had to give (except among Hungary's more conservative nobles ... and in Franz Joseph I's mind) - World War I was generally viewed as an opportunity for Austria to neuter its immediate enemies long enough to get its own house into order.
I'd actually say that, as much as Franz Joseph I helped keep the Empire together, he was as much a factor in its weakening over time. Under him, the old order ossified into place and the man was an arch-conservative - remember, he ascended to the throne in 1848. Having him die in, say, the 1905 assassination attempt might suffice - as Franz Ferdinand's ideas were largely in flux at this point and not as disastrous as they would become.