In 1815 Mount Tambora erupted throwing so much dust into the atmosphere that the year became known as "the year without a summer". *There were a few other mitigating factors but Tambora is thought to be the main culprit.
"This climate anomaly has been blamed for the severity of typhus epidemics in southeast Europe and the eastern Mediterranean between 1816 and 1819.The climate changes disrupted the Indian monsoons, caused three failed harvests and famine contributing to the spread of a new strain of cholera originating in Bengal in 1816. Many livestock died in New England during the winter of 1816–1817. Cool temperatures and heavy rains resulted in failed harvests in Britain and Ireland. Families in Wales travelled long distances as refugees, begging for food. Famine was prevalent in north and southwest Ireland, following the failure of wheat, oat, and potato harvests. The crisis was severe in Germany, where food prices rose sharply and demonstrations in front of grain markets and bakeries, followed by riots, arson, and looting, took place in many European cities. It was the worst famine of the 19th century"
In 1883 Kratotoa erupted and is known as the deadliest volcanic eruption in modern times. It threw so much sulphur and dust into the air that it caused temperatures to drop worldwide for ~5 years. At least 36 000 people died.
In the year following the 1883 Krakatoa eruption, average Northern Hemisphere summer temperatures fell by as much as 1.2 °C (2.2 °F). Weather patterns continued to be chaotic for years, and temperatures did not return to normal until 1888
The Krakatoa eruption injected an unusually large amount of sulfur dioxide (SO2) gas high into the stratosphere, which was subsequently transported by high-level winds all over the planet. This led to a global increase in sulfuric acid (H2SO4) concentration in high-level cirrus clouds. The resulting increase in cloud reflectivity (or albedo) would reflect more incoming light from the sun than usual, and cool the entire planet until the suspended sulfur fell to the ground as acid precipitation.
These are global cooling events but are not as extreme as nuclear winters or as if Yellowstone super volcano had erupted. There is no radioactive fallout, actually thinking about it there are probably trace amounts in the ejected tephra. This sort of chaotic event would not create a snowball earth scenario. I'm trying to avoid that.
In my story, I have a similar setup where several various factors intermingle and create a period of time with large to excessive amounts of dust in the atmosphere leading to cooler summers, colder winters and severe food shortages. People die, regimes fall, chaos ensues. But then the dust clears and life can resume.
I'm not aiming for long-term ice ages or anything as 'fixed' as that. I'm aiming for an extended period of chaotic weather (only a slight 1-2 degree average temperature difference) that will affect the stability of human food production that would further influence mankind's societies in the short-term.
Now for the question. Just how long can a society survive in such conditions? I have a minimum range of 5 - 10 years from Krakatoa and Tambora but society didn't fail in the real world. Yes, people died and moved around as refugees looking for food but I haven't found any mention of nation states breaking down. How much longer could such an event have lasted so that it could be the direct cause of a state breaking down. What is the maximum range; decades up to 50 years?
A sub question to help focus any answers. Would the ensuing climate chaos have to have a more severe effect over a shorter time period or can I just extend the duration of the climate chaos to decades to cause society failure? I have a feeling if the climate changes are just extended, surviving humanity will adapt and find new crops and contingencies to make do with.
Note: I haven't focused on the industrial level pre-disaster as I haven't figured that out yet. Several centuries after the event and my society in question is approaching or is already in the Renaissance. If this is the second enlightenment or the first I haven't decided yet. It all really depends on how intense the colder famine period was. Answers can take this into consideration.
Note: I do realise that the political situation will play a part in if the state fails or not. But I'm trying to figure out how long a state/society could theoretically survive with a damaged food production system before bringing political factors into play (which will help me narrow down the time period even more).