The emerging time-critical Internet-of-Things (IoT) use cases, e.g., augmented reality, virtual reality, autonomous vehicle, etc., involve computation-intensive tasks powered by artificial intelligence (AI) techniques. Due to the limited computation resource at IoT devices, it is challenging to fulfill the latency and reliability requirements. Offloading computation tasks using mobile-edge computing (MEC) are a promising solution. The service reliability in AI-powered time-critical services can be modeled by the transmission reliability, timeout probability, and inference accuracy. To improve service reliability, the state-of-the-art work emphasizes on transmission reliability and requires error-free transmission. We show that the AI-powered time-critical services can tolerate small image distortion and still remain the inference accuracy. Therefore, to improve service reliability, it is more important to minimize the timeout probability by shortening transmission latency than perfect error-free transmission. Motivated by this insight, we study the feasibility of user datagram protocol (UDP)-based offloading for such services in the MEC system. A prototype is developed and a series of experiments are conducted to understand how image distortion affects inference accuracy. We measure the latency and transmission reliability of transmission control protocol (TCP)-based and UDP-based offloading in real-life environments and evaluate the service reliability both experimentally and numerically. The evaluation results demonstrate that compared with the TCP-based offloading, the UDP-based offloading can improve the normalized service reliability by up to 70% for time-critical services. In addition, we propose an early termination of image reception (ETR) offloading scheme which can further improve the normalized service reliability by up to 10%, compared with the baseline UDP-based scheme.