There is often a latent period before the outbreak of financial crisis in enterprises, and reliable financial crisis warning is crucial for the stable development of enterprises. At present, significant achievements have been made in the field of financial crisis prediction, but the systematic research on the mechanism of financial crisis formation is still insufficient. This study aims to deeply analyze the formation mechanism of chronic financial crises, improve the accuracy of financial crisis warning by introducing a penalty logistic regression model, and provide a basis for enterprises to prevent, control, and overcome difficulties. This study uses the financial statement data of 2155 listed companies in Shanghai and Shenzhen from 2017 to 2024, and combines the three penalty functions of Lasso, SCAD and MCP to analyze these data. Through crossvalidation, this paper selects the optimal adjustment parameters, constructs a penalized logistic regression model, and compares it with the standard logistic regression model. Research has shown that the MCP penalty logistic regression model performs the best in accuracy (89.6 ± 0.8%), F1 score (0.852), AUC value (0.918), and other aspects, outperforming the standard logistic regression model and other penalty logistic regression models. The MCP model identified 15 important financial indicators that have a significant predictive effect on the company’s financial crisis. Overall, the financial crisis warning model combined with MCP penalty logistic regression performs well in prediction accuracy and variable selection ability, providing an effective financial crisis warning tool for enterprises.