We consider sensor data scheduling with communication energy constraint for remote state estimation over a time-varying fading channel. Given that the fade channel state with temporal correlated variation influences the estimation accuracy, the goal is to obtain a schedule for a sensor to decide whether using high energy to send its local estimate to a remote estimator in order to minimize the expected average estimation error covariance. By exploiting the feedback information, we propose an effective closed-form dynamic stationary scheduling scheme. We prove that such simple schedule is optimal in terms of the estimation performance by comparing with a general stationary schedule under energy constraint. Furthermore, we derive the sufficient and necessary condition for estimation stability when the sensor can only use low energy at each time. Numerical examples are provided to illustrate the effectiveness of the proposed scheme.