The robustness of Peer-to-Peer systems is challenged by its highly dynamic nature. Frequent peer failure and departure events introduce uncertainty for which is considered exceptional in traditional distributed systems. The difficulty of monitoring such large scale networks is further exacerbated because it has to be done in a completely decentralized way for both scalability and reliability concerns. Some methods for estimating peer failure rate have been applied in Peer-to-Peer systems, however their comparative performance has not yet been reported in the literature. We simulate three different failure rate estimation methods and compare their accuracy and response time with respect to sample size, stabilization interval and neighbour set size. We conclude that the Maximum Likelihood Method introduced is better than the Failure Frequency based Methods commonly used in current Peer-to-Peer systems.