Influence maximization is a fundamental research problem in social networks. Viral marketing, one of its applications, aims to select a small set of users to adopt a product, so that the word-of-mouth effect can subsequently trigger a large cascade of further adoption in social networks. The problem of influence maximization is to select a set of K nodes from a social network so that the spread of influence is maximized over the network. Previous research on mining top-K influential nodes assumes that all of the selected K nodes can propagate the influence as expected. However, some of the selected nodes may not function well in practice, which leads to influence loss of top-K nodes. In this paper, we study an alternative influence maximization problem which is naturally motivated by the reliability constraint of nodes in social networks. We aim to find top-K influential nodes given a threshold of influence loss due to the failure of a subset of R(<K) nodes. To solve the new type of influence maximization problem, we propose an approach based on constrained simulated annealing and further improve its performance through efficiently estimating the influence loss. We provide experimental results over multiple real-world social networks in support. This research will further support practical applications of social networks in various domains particularly where reliability would be a main concern in a system deployment.