A robust light storage and retrieval (LSR) in high dimensions is highly desirable for light and quantum information processing. However, most schemes on LSR realized up to now encounter problems due to not only dissipation, but also dispersion and diffraction, which make LSR with a very low fidelity. Here we propose a scheme to achieve a robust storage and retrieval of weak nonlinear high-dimensional light pulses in a coherent atomic gas via electromagnetically induced transparency. We show that it is available to produce stable (3+1)-dimensional light bullets and vortices, which have very attractive physical property and are suitable to obtain a robust LSR in high dimensions.