We investigate the dynamics of a non-linear network with noise, periodic forcing and delayed feedback. Our model reveals that there exist forcing regimes—called persistent entrainment regimes—in which the system displays oscillatory responses that outlast the termination of the forcing. Our analysis shows that in presence of delays, periodic forcing can selectively excite components of an infinite reservoir of intrinsic modes and hence display a wide range of damped frequencies. Mean-field and linear stability analysis allows a characterization of the magnitude and duration of these persistent oscillations, as well as their dependence on noise intensity and time delay. These results provide new perspectives on the control of non-linear delayed system using periodic forcing.