We examine the impact of independent agents failures on the solutions of cooperative games, focusing on totally balanced games and the more specific subclass of convex games. We follow the reliability extension model, and show that a (approximately) totally balanced (or convex) game remains (approximately) totally balanced (or convex) when independent agent failures are introduced or when the failure probabilities increase. One implication of these results is that any reliability extension of a totally balanced game has a nonempty core. We propose an algorithm to compute such a core imputation with high probability. We conclude by outlining the effect of failures on non-emptiness of the core in cooperative games, especially in totally balanced games and simple games.