Federated Learning (FL), arising as a novel secure learning paradigm, has received notable attention from the public. In each round of synchronous FL training, only a fraction of available clients are chosen to participate and the selection decision might have a significant effect on the training efficiency, as well as the final model performance. In this paper, we investigate the client selection problem under a volatile context, in which the local training of heterogeneous clients is likely to fail due to various kinds of reasons and in different levels of frequency. Intuitively, too much training failure might potentially reduce the training efficiency, while too much selection on clients with greater stability might introduce bias, and thereby result in degradation of the training effectiveness. To tackle this tradeoff, we in this paper formulate the client selection problem under joint consideration of effective participation and fairness. Further, we propose E3CS, a stochastic client selection scheme on the basis of an adversarial bandit solution, and we further corroborate its effectiveness by conducting real data-based experiments. According to the experimental results, our proposed selection scheme is able to achieve up to 2x faster convergence to a fixed model accuracy while maintaining the same level of final model accuracy, in comparison to the vanilla selection scheme in FL.