We study the problem of intermittent private information retrieval with multiple servers, in which a user consecutively requests one of K messages from N replicated databases such that part of requests need to be protected while others do not need privacy. Motivated by the location privacy application, the correlation between requests is modeled by a Markov chain. We propose an intermittent private information retrieval scheme that concatenates an obfuscation scheme and a private information retrieval scheme for the time period when privacy is not needed, to prevent leakage incurred by the correlation over time. In the end, we illustrate how the proposed scheme for the problem of intermittent private information retrieval with Markov structure correlation can be applied to design a location privacy protection mechanism in the location privacy problem.