Nonlinear, kinetic simulations of stimulated Raman scattering (SRS) under laser-fusion conditions present a bursting behavior. Different explanations for this regime have been given in previous studies: saturation of SRS by increased nonlinear Landau damping [K. Estabrook et al., Phys. Fluids B 1, 1282 (1989)], and detuning due to the nonlinear frequency shift of the plasma wave [H. X. Vu et al., Phys. Rev. Lett. 86, 4306 (2001)]. Another mechanism, also assigning a key role to the trapped electrons is proposed here: the breakup of the plasma wave through the trapped-particle instability.