We consider periodic sensor scheduling for remote state estimation under average transmission energy constraint. The sensor decides whether or not to send its data to a remote estimator in order to meet the transmission energy constraint. The transmitted data are likely to be dropped due to the imperfect communication. An optimal periodic schedule is found via the tools from the Markov chain. Furthermore, a sufficient condition of the system dynamics, energy budget, and packet drop rate, under which the remote estimator is guaranteed to be stable, is derived. Examples are provided to show the effectiveness of results.