I own a P20, not a P15, but I experienced my P20 shutting down under high wattage loads too. My understanding is that is by design to protect your equipment. This happened when I was running my P20, and all of my home theater equipment, from one 15 amp circuit (the P20 is not used to its maximum abilities with a 15 amp circuit). This “overload” situation prompted me to have two new 20 amp circuits installed, one that is dedicated for the P20. These new circuits were wired as “home runs” and the sound improvement was amazing! The P20 can now operate at full capacity with the 20 amp circuit. I also moved some equipment to the second 20 amp circuit and left other equipment on the original 15 amp circuit. Since adding the new circuits, I have not had anymore shutdowns. In your case, I don’t think that the zones on your P15 are the issue.
Here is a link to my post about my 20 amp circuits:
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