This technical note contributes to the convergence analysis for iterative learning control (ILC) for linear stochastic systems under general data dropout environments, i.e., data dropouts occur randomly at both the measurement and actuator sides. Data updating in the memory array is arranged in such a way that data at every time instance is updated independently, which allows successive data dropouts both in time and iteration axes. The update mechanisms for both the computed input and real input are proposed and then the update process of both inputs is shown to be a Markov chain. By virtue of Markov modeling, a new analysis method is developed to prove the convergence in both mean square and almost sure senses. An illustrative example verifies the theoretical results.