@kennethamy,
It's not so much particular cases but types of cases. I would think (and am no expert here) that there are types of situations to which the rules of classical logic can be applied very successfully - many such cases, in fact. I suppose, speaking intuitively, these are where the essential facts can be discerned, and the connection between the premisses and the conclusions reasonably ascertained.
But I think what has happened as society and knowledge have developed, is that we now often confronted with very complex, fluid, or chaotic situations, whether these be scientific, political, economic, or whatever. Market dynamics, or the way epidemics behave, or chaotic systems, often would seem to throw up problems that are not amenable to strictly logical analysis.
Also I think that Aristotlean logic in particular, and the laws of identity and the excluded middle and so on, really don't cope very well with 'the new physics' which is in fact one of the reasons that people are casting about for other logical and metaphysical systems within which they can be interpreted.
That is what I had in mind. I am just improvising here and anyone with more training in logic and so on may know a great deal more.