To address the issue of a launch vehicle failing to enter its target orbit due to a thrust drop fault, this paper proposes an online trajectory optimization method that integrates intelligent decision-making and convex optimization, aiming to enhance payload rescue efficiency. First, a joint optimization problem of the optimal rescue orbit and flight trajectory is formulated by relaxing terminal constraints and incorporating the weighted sum of the relaxation terms into the performance index. To determine the optimal weighting coefficients that minimize the energy consumption required for transferring the payload from the rescue orbit to the original target orbit, a deep neural network (DNN)-based weighting coefficients decision-making method is proposed. A nested optimization algorithm integrating particle swarm optimization (PSO) and sequential convex programming (SCP) is proposed to generate the datasets offline for training the DNNs. The optimal weighting coefficients and proper initial guesses are provided for the joint optimization problem using the trained DNNs in the online phase. Finally, numerical simulation results validate the effectiveness of the proposed method in significantly improving payload rescue capability.