Rogue waves are widely recognized as great threats to human oceanic activities. The effectiveness of using the Peregrine breather to model rogue waves has been successfully demonstrated in both numerical and physical wave tank. Additionally, its persistence in random seas has been confirmed in some cases, so that it can also be employed to model rogue waves in random seas. However, based on the results obtained by using the fully nonlinear numerical simulations in this paper, it is reported that the persistence of the Peregrine breather will be affected by the nonlinearities of the random seas, i.e., the spectral bandwidth and the background wave steepness. The investigation on the effects of the two parameters indicates that the Peregrine breather cannot persist thus may not be employed to model rogue waves in random seas in some cases. This paper provides knowledge about how to select background wave parameters, in order to model rogue waves by using the Peregrine breather, which can help saving significant time for designing the experiments.