Predicting the long-term lifetime of power MOSFET devices plays a central role in the prevention of unprecedented failures for power MOSFETs used in safety-critical applications. The various traditional model-based approaches and statistical and filtering algorithms for prognostics have limitations in terms of handling the dynamic nature of failure precursor degradation data for these devices. In this paper, a prognostic model based on LSTM and GRU is developed that aims at estimating the long-term lifetime of discrete power MOSFETs using dominant failure precursor degradation data. An accelerated power cycling test has been designed and executed to collect failure precursor data. For this purpose, commercially available power MOSFETs passed through power cycling tests at different temperature swing conditions and potential failure precursor data were collected using an automated curve tracer after certain intervals. The on-state resistance degradation data identified as one of the dominant failure precursors and potential aging precursors has been analyzed using RNN, LSTM, and GRU-based algorithms. The LSTM and GRU models have been found to be superior compared to RNN, with MAPE of 0.9%, 0.78%, and 1.72% for MOSFET 1; 0.90%, 0.66%, and 0.6% for MOSFET 5; and 1.05%, 0.9%, and 0.78%, for MOSFET 9, respectively, predicted at 40,000 cycles. In addition, the robustness of these methods is examined using training data at 24,000 and 54,000 cycles of starting points and is able to predict the long-term lifetime accurately, as evaluated by MAPE, MSE, and RMSE metrics. In general, the prediction results showed that the prognostics algorithms developed were trained to provide effective, accurate, and useful lifetime predictions and were found to address the reliability concerns of power MOSFET devices for practical applications.