This is a very interesting and important question. Is there a general trend for how robustness scales with complexity? For evolved species, there will probably be an answer that depends on their population size and reproductive strategy. For constructed things like civilizations, the answer will probably be different. Gotta run but I'll edit this comment later.
Is there a general trend for how robustness scales with complexity?
I think the general answer is the useless one: "it depends", but for the particular case of the contemporary high-tech society I get a feeling (a "prior" in local lingo) that the robustness is negatively correlated with complexity.
A notable recent example: the 2008 financial crisis.
Yesterday I was using the Global Terrorism Database to check some suprisingly low figures on what percentage of terrorist acts are committed by Muslims. (Short answer: Worldwide since 2000, about 80%, rather than 0.4 - 6% as given in various sources.) But I found some odd patterns in the data for the United States. Look at this chart of terrorist acts in the US which meet GTD criteria I-III and are listed as "unambiguous":