There is always the tank story/myth http://neil.fraser.name/writing/tank/. Of course, that is more about how a neural network might not be training itself in the way you expect.

This was more a case of the training data not being representative of the actual domain (since Google changed the domain before the presentation). If it were a case of overfitting, the system wouldn't have had the accuracy it had, since it wouldn't work well for data outside the training set.

It becomes less able to generalize and its accuracy drops.