The Cold War. On at least one known occasion, and likely some we don't know about, an individual decided that "nah, that's not a real nuclear attack, that's some malfunction in the detection system."

Arguably also the Great War, when on successive occasions the Russian, Italian, French, and finally German armies decided that they weren't going to fight this way any more. Although perhaps this doesn't really match your question, since it (as far as I can tell) wasn't killing they objected to.