I can say a little about automobile alternators. They are normally designed with a 40% freeboard. A 100 amp alternator will "freeboard", or make an excess of 40 amps beyond the vehicle's needs. My Chevy Blazer came stock with a 110 amp alternator, but used about 70 amps to run the truck. There are Hondas with 35 amp alternators, not a great candidate for a high end build.
The capacitor I'm guessing is on your power in line? The big red wire from + on your battery. Capacitors oppose a change in voltage by storing electrons which it releases to make up for drops in supplied voltage caused by excess demand, like a huge bass hit. If you are drawing big power (currents get very high in a 12volt system, they have to because the voltage is so low) there may be a sensor in the deck's power supply for low voltage/current conditions to protect the circuitry, not that big of a reach for a high end deck. BTW the cap should be as close to your biggest amp as possible.
Good info, but helpful, IDK.
My 2 cents? If it was working, something broke. A loose, broken connection like that huge plug for the back of the radio that can get loose from shaking if the strap to the frame has not been installed (kinda normal). If it is something you just put together and it never worked right, look in the mirror. check your wiring and the tightness of your connections. The crimpons are pretty notorious for bad connections.
You said it cuts out when you accelerate (draw power!) and get a bass hit (I need MORE power Scotty!!). And that cap is there for a reason (Keep voltage high).
1. I would put a sensitive voltage meter on the +, you can jump off the cig lighter temporarily and go for a ride, get that bass pumping, see how line voltage reacts. Anything under 12 is killing your battery and alternator and probably turning off your deck.
2. if your line voltage is jumping severely, the cap is faulty or not working (bad connection). is it new? and what is the lifetime of a cap, they do leak, there is a dielectric fluid inside separated by two plates (rolled up tin foil lol) and suffer in the heat a bit, like in a car trunk.
3. It's possible your drawing more power than you can provide and you can't get something for nothing. Are you driving a Honda?
Good luck, hope that helps, if not, don't be shy, give me a shout deadkennedy, however that gets done around here, I'm kinda new. A few more clues, I can give better answers.