Why do my subs turn off at high volume in my car?

Either your amp gains are set too high or its at a lower ohm load than rated/ recommended. It has nothing to do with not enough power since you Have multiple batts. You dont need a cap, correction, you'll never need a cap. Batteries are more efficent and supply more power than a cap could hope to supply. Wire are always a factor, if you do not have the right gauges for the application, then upgrade your wires. You should get the amps set professionally. Take it to a car audio shop (not bestbuy) and have them set your amps for you.