Messaging services are a useful component in distributed systems that require scalable dissemination of messages (events) from suppliers to consumers. These services decouple suppliers and consumers, and take care of client registration and message propagation, thus relieving the burden on the supplier. Recently performance models for the configurable delivery and discard policies found in messaging services have been developed, that can be used to predict response time distributions and discard probabilities under failure-free conditions. However, these messaging service models do not include the effect of failures. In a distributed system, supplier, consumer, and messaging services can fail independently leading to different consequences. In this paper we consider the expected loss rate associated with messaging services as a performability measure and derive approximate closed-form expressions for three different quality of service settings. These measures provide a quantitative framework that allows different messaging service configurations to be compared and design trade-off decisions to be made.