With the advance of emerging digital twin (DT) technology, the combination of DT with edge intelligence brings great potential for high-fidelity, delay-sensitive inference services at the network edge. Due to the training data drift over time, the accuracy of an inference model degrades dramatically. To maintain and/or enhance its accuracy, the service model requires to be continuously retrained using newly generated update data. However, model retraining and inference services compete with each other for the limited computing resource in a mobile edge computing network (MEC), which may decrease user satisfaction with services due to unbearable service delays caused by insufficient resource supplies. Therefore, to ensure high fidelity of service models by choosing models for retraining while maximizing user satisfaction, it becomes a great challenge to allocate the limited computing resource in an MEC to both model retraining and inference services. In this paper, we investigate fidelity-aware, delay-sensitive services in a DT-assisted MEC network over a given time horizon. We study a novel user satisfaction maximization problem with the aim to maximize the long-term user satisfaction on services. We first formulate an integer linear programming (ILP) solution to its offline version. We then devise an online algorithm for the problem with a bounded expected cumulative regret, by leveraging an efficient prediction mechanism and a multi-armed bandit (MAB) based resource allocation strategy. Finally, we evaluate the performance of the proposed algorithm via simulations. Simulation results demonstrate that the proposed algorithm is promising, outperforming the comparison benchmarks.