Developing communication standards highlight a scenario called massive Machine-Type Communication within the framework of the Internet of Things. Under this scenario, a large number of devices with autonomous power supplies will operate in a random multiple access mode. It is crucial to keep the system stable, while consuming minimal energy. We describe a model of a system with a Gaussian Random Access Channel and consider an algorithm allowing message retransmissions. We provide a stability condition for the system and introduce an optimization problem to determine an achievability bound for energy per bit.