Modulation patterns are known to carry critical predictive cues to signal detection in complex acoustic environments.  The current study investigated the persistence of masker modulation effects on post-modulation detection of probe signals.  Hickok et al. (2015) demonstrated that thresholds for a tone pulse in stationary noise follow a predictable periodic pattern when preceded by a 3-Hz amplitude modulated masker.  They found entrainment of detection patterns to the modulation envelope lasting for approximately 2 cycles after termination of modulation.  The current study extends these results to a wide range of modulation rates by mapping the temporal modulation transfer function for persistent modulatory effects.  We found significant entrainment to modulation rates of 2 and 3 Hz, a weaker effect at 5 Hz, and no entrainment at higher rates (8 to 32 Hz).  The effect seems critically dependent on attentional mechanisms, requiring temporal and level uncertainty of the probe signal.  We also investigated whether entrainment extends to more complex periodic patterns by using driving modulators comprising two simultaneous rates (2 & 3 Hz or 3 & 5 Hz).  No persistence was observed for these complex patterns.  Our findings suggest that the persistence of modulatory effects on signal detection is lowpass in nature and attention based, extending only to simple envelope patterns.