If its a case of asking the receiver to do too much, you'll have to play at lower volumes.
Does it do it during movies, or does it do it randomly, even when nothing is being played though it? If its random even when not in use, unplug all interconnecting cables and speaker cables and see if it still cuts out when it's only plugged into the mains. If it does, it's an internal problem.
One thing you could try - what is the crossover frequency for your sub? If its low (40-60Hz for example) try upping it to about 80Hz. If its already around the 80Hz mark, try 100Hz. Impedance generally drops at lower frequencies, so you'll be easing the load on your receiver. If it still does it, you'll need something more powerful.