The intrinsic structural stability of ABO₃ perovskite materials is a pivotal factor determining their efficiency and durability in photovoltaic applications. However, accurately predicting stability, commonly measured by the energy above hull metric, remains challenging due to the complex interplay of compositional, crystallographic, and electronic features. To address this challenge, we propose a streamlined hybrid machine learning framework that combines the sequence modeling capability of Long Short-Term Memory (LSTM) networks with the robustness of Random Forest regressors. A genetic algorithm-based feature selection strategy is incorporated to identify the most relevant descriptors and reduce noise, thereby enhancing both predictive accuracy and interpretability. Comprehensive evaluations on a curated ABO₃ dataset demonstrate strong performance, achieving an $R^2$ of 0.98 on training data and 0.83 on independent test data, with a Mean Absolute Error (MAE) of 8.78 for training and 21.23 for testing, and Root Mean Squared Error (RMSE) values that further confirm predictive reliability. These results validate the effectiveness of the proposed approach in capturing the multifactorial nature of perovskite stability while ensuring robust generalization. This study highlights a practical and reliable pathway for accelerating the discovery and optimization of stable perovskite materials, contributing to the development of more durable next-generation solar technologies.