In model-based state of charge (SOC) estimation for lithium-ion batteries, data collected by sensors are crucial for accurate SOC estimation. In practical applications, random sensor failures may lead to data loss, which can seriously affect the accuracy of SOC estimation. To address this problem, a method based on a variable recursive interval correction auxiliary model with stochastic gradient is proposed. First, a normal distribution parameter is introduced to simulate random sensor failures. Second, under conditions of data loss, a sequence of integers representing known data points is defined, and the unobservable data are obtained using a variable recursive interval approach. The unknown information vector parameters are then compensated through a correction auxiliary model stochastic gradient iterative algorithm. Finally, a convergence index and forgetting factor are introduced into parameter identification to improve convergence speed and accuracy. Experimental results show that the proposed method achieves a mean absolute error within 2.5% under various operating conditions and different data loss rates, demonstrating strong robustness.