Submersible motors are widely used in oil fields, and vibration data are commonly employed for motor fault detection. Due to the limited sample size of fault data in submersible motors, traditional machine learning methods exhibit poor performance. In this study, we propose a method for fault diagnosis of submersible motors under small sample conditions. We utilize Long Short-Term Memory (LSTM) networks to handle the time series data and combine them with autoencoders to automatically extract vibration signal features. To address the issue of effective feature extraction in the presence of noise, we improve the loss function of the LSTM autoencoder by incorporating L2,1 norm regularization. Compared to traditional LSTM and AE anomaly detection methods, our approach achieves higher accuracy with a precision of 99.1%.