Durability describes the ability of a device to operate properly in imperfect conditions. We have recently proposed a novel neural network structure called an “Affordable Neural Network” (AfNN), in which affordable neurons of the hidden layer are considered as the elements responsible for the robustness property as is observed in human brain function. Whereas earlier we have shown that AfNNs can still generalize and learn, here we show that these networks are robust against damages occurring after the learning process has terminated. The results support the view that AfNNs embody the important feature of durability. In our contribution, we investigate the durability of the AfNN when some of the neurons in the hidden layer are damaged after the learning process.