In this paper, we formulate a long-term resource allocation problem of non-orthogonal multiple access (NOMA) downlink system for the satellite-based Internet of Things (S-IoT) to achieve the optimal decoding order and power allocation. This long-term resource allocation problem of the satellite NOMA downlink system can be decomposed into two subproblems, i.e., a rate control subproblem and a power allocation subproblem. The latter is a non-convex problem and the solution of which relies on both queue state and channel state. However, the queue state and the channel state continually change from one time slot to another, which makes it extremely strenuous to characterize the optimal decoding order of successive interference cancellation (SIC). Therefore, we explore the weight relationship between the queue state and the channel state to derive an optimal decoding order by leveraging deep learning. The proposed deep learning-based long-term power allocation (DL-PA) scheme can efficiently derive a more accurate decoding order than the conventional solution. The simulation results show that the DL-PA scheme can improve the performance of the S-IoT NOMA downlink system, in terms of long-term network utility, average arriving rate, and queuing delay.