The Man 986

Hey,
I have 2 12 jl audio w0s hooked up to a jl audio 500/1 amp and Ive had it hooked up for a while now. It isnt hooked up to an after market head unit but the factory stuff. It works fine untile A hard type of bass hits and suddenly it cuts off then cuts back on right after like 2 seconds. I had a capacitor put in and my lights dont dim so I know it isnt a battery problem, I turned the amp down a little and it still does it, but It seems as if the amp doesnt shut off cause the green light stays on. I was thinking that maybe the amp was to powerful for the w0s thus it has some sort of safety when a certain amount of bass hits. Well any suggestions?? Should I get w3s to make it handle the amp better or what?? anything would help...thanx