Stable employment is a pivotal foundation for contemporary economic development and transformation. The enhancement of labor contract relationship stability is crucial for the great rejuvenation of the Chinese nation. Drawing from civil law and various research materials, this study identifies key factors influencing labor contract stability and posits several research hypotheses. This paper constructs a regression analysis model to examine the relationships between these factors and labor contract stability, where the influencing factors serve as independent variables and the stability of the labor contract relationship acts as the dependent variable. The model’s fit is rigorously evaluated. A preliminary analysis employing Pearson’s correlation coefficient reveals significant correlations between all 14 identified factors and the stability of labor contract relationships, supporting the use of regression analysis. Empirical results from the regression analysis indicate a significant positive impact of education level on labor contract stability (p = 0.031 < 0.05). Similarly, employment income is shown to positively influence labor contract stability (p = 0.009 < 0.05). Apart from education level and urban integration challenges, other identified factors also significantly affect the stability of labor contracts. This research not only advances our understanding of the dynamics influencing labor contract stability but also provides a robust empirical basis for shaping relevant civil law regulations and policies.