Significance Understanding the relaxation dynamics on complex energy landscapes is a key aspect not only for physical processes but also for many applications where the minimization of a complicated cost function is required. Mean-field models with disorder have been and still are the privileged playing field to try to understand such complex dynamical behavior. We report the results of extraordinary long numerical simulations (more than 2 64 spin updates) of the prototypical mean-field model of spin glasses. We uncover that, contrary to common expectation, the off-equilibrium aging dynamics at low temperatures undergoes a strong ergodicity breaking and thus asymptotically remains trapped in a confined region of the configurational space. Our results ask for a fundamental revision of models for the aging dynamics.