Applications requiring massive connectivity, such as the Internet of Things and vehicular networks, pose challenges for time-division-duplex (TDD) massive multiple-input multiple output (MIMO) systems due to the increasing overhead of channel state information (CSI) acquisition. By exploiting the temporal correlations of user channels, we propose an intermittent channel estimation (ICE) scheme to maximize the sum achievable rate in such applications. The limited pilot resources should be carefully assigned to users with heterogeneous mobility, which is formulated as a multichain Markov decision process (MDP). The optimal pilot pattern is then obtained as the solution of the MDP. Furthermore, to reduce the computational complexity of the MDP, we relax the constraint of the pilot pattern design problem and convert it into a convex optimization problem, whose solution has close-to-optimal performance. Our simulation results show that the ICE scheme can significantly outperforms the conventional scheme which persistently updates the CSI of all users.