To echo Conifold's comment, the example you give is not a pure case of an Aristotelean syllogism. It involves a real world object called a ball which is assumed to persist unchanged over time and it refers to an action of taking a ball out of a box, which also tacitly assumes that this action has no effect on the ball.
In practice, if we found that we could draw red balls from the box, having only put white ones in, we would make some guesses such as that some mischievous person is managing to swap the balls without our seeing it, or the balls are designed to change colour after a period of time, or the balls are sensitive to temperature and may change colour when touched, or maybe even that the balls interact with the box in some weird way and change colour when removed from it. We would then want to test these guesses by reproducing the results in different experiments.
However, I understand your unlying point, which I take to be that if we abstract away from the details of this particular example, is there some circumstance in which we might judge our logic itself to be wrong?
We can pick up a useful idea from Quine. Think of our beliefs as being connected together in a web. The intersection points are specific beliefs that we have, and the strands that connect them and hold them together are the various generalisations and laws that we believe hold good. If we change one of our beliefs, that change will propagate changes to neighbouring beliefs in order to ensure consistency. Some of our beliefs are more readily exposed to change than others: they are closer to the edge of the web where our beliefs interact with empirical reality.
For example, I believe that my car is parked in my garage, but if a policeman knocked on my door and informed me that it had been stolen, I would readily revise that belief, and a few others about the current state of the car and the amount of unoccupied space in my garage. Other beliefs are less susceptible to revision. They are more deeply entrenched because they depend on a great many observations by several people. It would be more difficult to get me to revise my belief that eating meat is a healthy thing to do, though not impossible. It would be more difficult still to persuade me that some well established law of nature is wrong. But again, not impossible. Sometimes science progresses by discovering that previously held theories are wrong, but the evidence had better be really good.
These deeply entrenched beliefs can be pictured as being near the centre of the web. They are held in place by so many strands that we cannot revise them without making lots of changes elsewhere. When we do make a revision, we do so roughly in accordance with a principle of minimum mutilation. We keep the changes as small as we can, consistently with accommodating the new information. Revising our belief in a law of nature is a big deal and we don't want to do it if we can find some simpler change that covers the observations.
So one way of understanding your question is: could we envisage a situation in which the empirical evidence that presents itself to us is so extremely different from what we can account for in normal ways, that we might contemplate not just revising our understanding of the laws of nature, but actually revising our understanding of logic itself?
Different logicians have given different answers to this question. Traditionally, logic has been regarded as iron-clad laws that our thoughts are obliged to conform to. This idea is less popular than it used to be. Quine himself thought that logic could in principle be revisable in the light of empirical evidence, though he was so firmly attached to classical logic that he considered it infeasible in practice. Hilary Putnam conjectured that we might revise logic in the light of quantum mechanics, though his proposed quantum logic never caught on.
One modern approach to understanding logic is to think of logics (for there are many) as tools that we use to organise and systematise information and to render it into a deductive formalism. There is no compelling reason in general to suppose that a single tool will work everywhere and perform all such tasks adequately. Classical logic, for example, has issues with vagueness, future contingents, and undecidable propositions in mathematics. Could there be situations where one particular logic does not apply? Yes. Could there be some situations where no logic would apply? It is difficult to see how, but maybe we are just reaching the limits of our imagination, not the limits of possibility. Could we envisage logics not working at all anywhere? Hardly. It would seem to imply a situation that would be so chaotic (in the informal sense) that living things like us wouldn't be there to observe it.