How your car audio system works is dependent on exactly how it has been wired up.
What power source is powering your amp?
What 'ACC' wire are you using to turn on the amp?
How exactly is the head unit connected to the speakers and amp?
We could be more helpful if you can provide some photos of your installation.
Just going by what you have explained briefly, it is wired incorrectly. It seems you are sourcing your power from a bridged/low end gauge wire which may run fine whilst there is little to no current draw on the vehicles electrical system (ECU/Lights/Etc), as soon as you 'run' the vehicle, the current draw on that circuit is in full use and unstable as the vehicles electrical system is using most of it, the voltage fluctuates and causes the amp to trip out (protect mode).
For a power amplifier to run proper and not overload circuits, it will require its own independent power source... that being an 8 gauge (or 4 gauge) ~60amp fused power connection run directly from the battery terminal to your amplifier, as well as the the same gauge earth/chassis connection. The blue 'remote' wire will run from the back of your head unit directly to the amplifier, so when the head unit turns on, it also powers up your amplifier. You can even go as far as also adapting in a capacitor should your voltages fluctuate still... this will keep the audio system sounding great via the constant stable voltage provided.