This paper focuses on the application of meta-reinforcement learning to the robust design of low-thrust interplanetary trajectories in the presence of multiple uncertainties. A closed-loop control policy is used to optimally steer the spacecraft to a final target state despite the considered perturbations. The control policy is approximated by a deep recurrent neural network, trained by policy-gradient reinforcement learning on a collection of environments featuring mixed sources of uncertainty, namely dynamic uncertainty and control execution errors. The recurrent network is able to build an internal representation of the distribution of environments, thus better adapting the control to the different stochastic scenarios. The results in terms of optimality, constraint handling, and robustness on a fuel-optimal low-thrust transfer between Earth and Mars are compared with those obtained via a traditional reinforcement learning approach based on a feed-forward neural network.