In social networking services (SNSs), persistent topics are extremely rare and valuable. In this paper, we propose an algorithm for the detection of persistent topics in SNSs based on Topic Graph. A topic graph is a subgraph of the ordinary social network graph that consists of the users who shared a certain topic up to some time point. Based on the assumption that the time evolutions of the topic graphs associated with persistent and non-persistent topics are different, we propose to detect persistent topics by performing anomaly detection on the feature values extracted from the time evolution of the topic graph. For anomaly detection, we use principal component analysis to capture the subspace spanned by normal (non-persistent) topics. We demonstrate our technique on a real dataset we gathered from Twitter and show that it performs significantly better than a baseline method based on power-law curve fitting, the linear influence model, ridge regression, and Support Vector Machine.