The proliferation of demanding applications and edge computing establishes the need for an efficient management of the underlying computing infrastructures, urging the providers to rethink their operational methods. In this paper, we propose an Intelligent Proactive Fault Tolerance (IPFT) method that leverages the edge resource usage predictions through Recurrent Neural Networks (RNN). More specifically, we focus on the process-faults, which are related with the inability of the infrastructure to provide Quality of Service (QoS) in acceptable ranges due to the lack of processing power. In order to tackle this challenge we propose a composite deep learning architecture that predicts the resource usage metrics of the edge nodes and triggers proactive node replications and task migration. Taking also into consideration that the edge computing infrastructure is also highly dynamic and heterogeneous, we propose an innovative Hybrid Bayesian Evolution Strategy (HBES) algorithm for automated adaptation of the resource usage models. The proposed resource usage prediction mechanism has been experimentally evaluated and compared with other state of the art methods with significant improvements in terms of Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE). Additionally, the IPFT mechanism that leverages the resource usage predictions has been evaluated in an extensive simulation in CloudSim Plus and the results show significant improvement compared to the reactive fault tolerance method in terms of reliability and maintainability.