Large scale decentralized systems, such as P2P, sensor or IoT device networks are becoming increasingly common, and require robust protocols to address the challenges posed by the distribution of data and the large number of peers belonging to the network. In this paper, we deal with the problem of mining frequent items in unstructured P2P networks. This problem, of practical importance, has many useful applications. We design P2PSS, a fully decentralized, gossip--based protocol for frequent items discovery, leveraging the Space-Saving algorithm. We formally prove the correctness and theoretical error bound. Extensive experimental results clearly show that P2PSS provides very good accuracy and scalability, also in the presence of highly dynamic P2P networks with churning. To the best of our knowledge, this is the first gossip--based distributed algorithm providing strong theoretical guarantees for both the Approximate Frequent Items Problem in Unstructured P2P Networks and for the frequency estimation of discovered frequent items.