Through one-dimensional and two-dimensional (2D) particle-in-cell simulations of stimulated Raman scattering (SRS), we show that nonlinear plasma wave packets that are created during SRS and convect through the system after saturation can have a dramatic effect on the recurrence of the instability. The recurrence rate is shown to depend on the propagation speed and frequency content of these packets. Furthermore, SRS can be driven to higher amplitudes via backscattered light traveling between packets. In 2D, the influence of the plasma wave packets is also seen, but the average reflectivity is substantially less due to geometric effects and transverse localization of the packets.