Nearly all adaptive control techniques require that the control directions of dynamical systems are known in advance. In this paper, for a class of pure-feedback nonaffine discrete-time systems with unknown control directions (UCDs), a high-order neural network (HONN)-based adaptive iterative learning control (ILC) approach is presented to address a repetitive tracking control issue. The implicit function theorem is adopted to cope with the difficulty resulting from the nonaffine structure of control input. Employing a discrete Nussbaum-type function in the neural network weight adaptation law to suit the UCD, an HONN is used to iteratively estimate the ideal control signals. In addition, a novel dead-zone method is developed in the HONN-based adaptive ILC algorithm to enhance its robustness against nonrepetitive desired trajectories and random uncertainties in iterative initial errors and external disturbance. Consequently, the system output, except at the initial n time instants, is demonstrated to asymptotically converge to an adjustable range of the desired trajectory along the iteration axis, while all of the system signals remain bounded during the entire ILC process. Two simulation examples show the feasibility of the adaptive ILC approach.