The insulation paper loss of life (LOL) of a distribution transformer (DT) is largely determined by its winding hot-spot temperature. It is mainly estimated via the transformer load, ambient temperature, and related physical parameters. Fortunately, advanced metering infrastructure (AMI) can provide load profiles of DTs, allowing a cost-effective LOL estimation solution. However, the AMI dataset contains measurement errors that significantly reduce LOL estimation accuracy. A forecasting method is needed to recover the erroneous AMI data. This is a challenging problem, as the load profiles of DTs are nonstationary and volatile. We propose an ensemble of stacked long short-term memory (ES-LSTM) networks to simultaneously capture load consumption patterns of DTs and their correlations. The ES-LSTM consists of two independent LSTM networks and a feed-forward neural network (FFNN) stacked on top of them. A two-stage training procedure is applied. In the first stage, two LSTM networks are trained to capture the daily or weekly load patterns. In the second stage, the FFNN is trained to optimally combine the last hidden outputs of the two LSTM networks. Field verification is conducted using real AMI data obtained from an urban distribution utility in China. The test results confirmed the superiority of the proposed method.