Due to the technology evolution, one of the main problems for future System-on-Chips (SoC) concerns the difficulties to produce circuits without defaults. While designers propose new structures able to correct the faults occurring during computation, this article addresses the control part of SoCs, and focuses on task scheduling for processors embedded in SoC. Indeed, to ensure the execution of application in presence of faults on such systems, operating system services will need to be fault tolerant. This is the case for the task scheduling service, which is an optimization problem that can be solved by Artificial Neural Network. In this context, this paper explores the intrinsic fault tolerance capability of Hopfield Artificial Neural Network (HANN). Our work shows that even if some neurons are in fault, a HANN can provide valid solutions for task scheduling problem. We define the intrinsic limit of fault tolerance capability of Hopfield model and illustrate the impact of fault on the network convergence.