System shutting down due to clipping?

For some Yamaha AVRs, there is a setup option to run "6-ohm" speakers (which may work 'better' for your 4-ohm speakers).

Check your manual.

Also check to see what your max volume setting is: there are options to limit the volume and if you don't have that set to max then the AVR may shut down as well.

Check your manual.

Not knowing the receiver or speakers, at least make sure the surrounds are set to small. The fronts also, if the subwoofer handles the bass.

What you're saying is that you refuse to purchase nail proof tires or drive around the nails in the driveway.

If you're pushing your equipment beyond it's limits then the only solution is to purchase equipment that'll do what you want. If you don't, you can expect problems and eventually it'll shorten the life of the AVR and will turn into a self solving problem unless you replace it with another unit that's not up to the task.

Try running the setup without the rear channels and see if it still trips off. This would help isolate the problem. If your center is also 4 ohms then bypass that one as well.

Why are you asking if you're not willing to do anything about it?