This is totally opinion, but when i had my kenwood cd player, and i was running my sub off the rcas. When i turned on rap with somewhat medium volume, it would shut off and then restart. It had an auto-protect mode when i tried to send too much power through it. Sounds like your having the same problem. Your head unit is not powerful enough to push those speakers so its trying to work to hard. My thought would be, add whichever is cheaper, a amp plus all the wiring and such, or get a better head unit. I imagine it never shuts off at lower volumes? just when u got it blasted?