The distributed inference framework is an emerging technology for real-time applications empowered by cutting-edge deep machine learning (ML) on resource-constrained Internet of things (IoT) devices. In distributed inference, computational tasks are offloaded from the IoT device to other devices or the edge server via lossy IoT networks. However, narrow-band and lossy IoT networks cause non-negligible packet losses and retransmissions, resulting in non-negligible communication latency. This study solves the problem of the incremental retransmission latency caused by packet loss in a lossy IoT network. We propose a split inference with no retransmissions (SI-NR) method that achieves high accuracy without any retransmissions, even when packet loss occurs. In SI-NR, the key idea is to train the ML model by emulating the packet loss by a dropout method, which randomly drops the output of hidden units in a DNN layer. This enables the SI-NR system to obtain robustness against packet losses. Our ML experimental evaluation reveals that SI-NR obtains accurate predictions without packet retransmission at a packet loss rate of 60%.