In this article, we study the tracking problem for networked nonlinear discrete systems with actuator faults and dual-direction data dropouts. A novel adaptive fault-tolerant iterative learning model-free control strategy is designed. First, by utilizing the method called compact form dynamic linearization, the original nonlinear system model is transformed into an equivalent data-driven model, and the data model contains only one unknown parameter. Both the actuator fault and the system dynamics information are included in this parameter. Then, to model the physical processes of data dropout, a new mathematical relationship is constructed. Furthermore, an adaptive fault-tolerant iterative learning tracking control scheme is developed with only randomly received input/output data. Noting that the high learning rate or convergence rate is required in actual applications, a new varying parameter approach is designed to improve such rate. Finally, it is rigorously proved that the closed loop is stable in the sense of uniform ultimate boundedness, and numerical simulation results are conducted to validate the effectiveness of the designed control strategy.