hey had this exact problem with an L7 and a kicker kx1200.1
it was the amp...it wasnt getting enough power so it would shut off.....kicker amps are real gay like that. We upgraded the wires on my friends car and it completely fixed the problem. Make sure ur positive lead wire is connected straight to the battery too and not one of those jump start places.
hope i helped you and im sure this is what the problem is man
You can test it like this.......turn ur car on, and leave the air conditioner off.....turn it up, then turn the air conditioner on, in a very short about of time ur subs will start to play then pop on and off. (its annoying as hell and sounds like they are gonna blow up or somthin haha)