Try a different player (CD, DVD, etc whatever) into the amp and see if the amp exhibits the same behavior at the same relative volume. If this 'fixes' it, then the issue is neither the input nor output sections of the amplifier.
Hopefully this next part makes sense -- Like most things, a player's output voltage is RMS. So when it's coasting along you'll experience its normal rated output and everything's ok. But on dynamic peaks you can hit output moments potentially 300% higher, and if it's turned way up this can saturate the input section of the downstream device. That strictly speaking wouldn't be the downstream device's fault, either. Such a peak is way out of range. The 'fix' there would be to turn down the volume (gain/output level) of the player device and compensate by a higher volume on the amplifier. (Or by not listening as loud, or by having more sensitive speakers).
If it's the output section of the amplifier, you should hear quite a bit of distortion (Clipping) before getting any Cutouts. -- Distortion there would be what's called Clipping (as reproduction of the the waveforms get clipped off at the peaks). Beyond this level of overdrive you might get Cutouts from an amp's output section but the distortion/clipping should give quite a bit of warning before that point.