As Deep Learning (DL) continues to be widely adopted, the growing field of study on the robustness of DL approaches in finance is gaining steam. This paper investigates the robustness of a Recurrent Neural Network (RNN) with Long Short-Term Memory (LSTM) intended for daily closing price predictions of Bitcoin (BTC). The research entails reproducing and adjusting an LSTM design from previous research, with an emphasis on evaluating the robustness of the network. The network is trained using data that has been disturbed by Gaussian noise to assess robustness, and the effect on predictions made outside of the sample is examined. To examine the impact of adding Gaussian noise layers and noisy dense layers on training accuracy and out-of-sample predictions, further robustness tests are conducted. The results show that the LSTM network has remarkable robustness to random disturbances in the data. Nevertheless, the Root Mean Square Error (RMSE) of the prediction increases with the addition of Gaussian noise and noisy dense layers. When random noise is present in the training data, the Autoregressive Integrated Moving Average (ARIMA) model is more vulnerable to it than the LSTM, according to the robustness of the two models. These findings highlight how robustness DL techniques are overall when compared to more conventional linear methods. However, because these models are black-box, the study highlights the significance of comprehensive testing. Although the robustness of the LSTM is impressive, it is important to understand that each network may behave differently depending on the circumstances.