Shifts in data distribution across time can strongly affect early classification of time-series data. When decoding behavior from neural activity, early detection of behavior may help in devising corrective neural stimulation before the onset of behavior. Recurrent Neural Networks (RNNs) are common models to model sequence data. However, standard RNNs are not able to handle data with temporal distribution shifts to guarantee robust classification across time. To enable the network to utilize all temporal features of the neural input data, and to enhance the memory of an RNN, we propose a novel approach: RNNs with time-varying weights, here termed Time-Varying RNNs (TV-RNNs). These models are able to not only predict the class of the time-sequence correctly but also lead to accurate classification earlier in the sequence than standard RNNs. In this work, we focus on early robust sequential classification of brain-wide neural activity across time using TV-RNNs as subjects perform a motor task.