Duh... Your running a subwoofer off a factory head unit!!
Prolly clipping the holy h e l l out of it too! break out the xtra cash n buy a some wiring and buy a separate amplifier for the sub...
He says he has an amp.
To the op, when the amp cuts out check your voltages at the remote and power wire and see if the protect light is on. It's just weird as hell that it's at the same time interval. It's almost like the power supply section can't handle the juice.