Check your ground. Is it grounded to the chassis or to the stock ground wire? Are you using your stock wiring harness? Improper wiring will shut down the unit under the load if it cant get the required voltage. I would first check your ground and try grounding it to the chassis. If that doesnt work check to see if your positive wire is properly connected. Did you use electrical take or proper butt connecters / solder ?
Personally I hate stock wiring so I run a 10g wire from my battery direct to the deck/stereo. The stock wiring is cheap and very thin and made to handle a very little powered stock radio. Thats all I got, hope it helped!