Predicting the Remaining Useful Life (RUL) or the Time of Failure (ToF) is the main concern of predictive maintenance. Accurately predicting the RUL for systems with small datasets is challenging. To solve the problem of low RUL prediction accuracy in such cases, a novel approach based on machine learning is proposed to accurately predict the RUL of systems with limited data. The proposed system implements a self-adaptive Neural Network (NN), where a feedback mechanism is added to the NN architecture to improve the model training with updated features. The prognosis system is validated using real data collected from oil and gas wells during production to predict the ToF of a Subsurface Safety Valve system. To simulate the tool being in service, only fractions of data are given to the prediction model, the predictions are fitted using a curve-fitting function to estimate the intersection between the estimation and the x-axis (ToF). Experimental results showed the positive effect of the proposed approach in improving prediction accuracy for systems with insufficient data; experimental evaluation has been conducted in terms of Mean Square Error and RUL absolute estimation error showing an improvement compared to the baseline approach.