If your amp is the Kenwood KAC-8103D, it is rated at 500 watts RMS into a 2 ohm load. Your vehicle electrical system should be able to provide plently of current even without a capacitor. But over time wires corrode, the alternator doesn't work as well as when new, and even the battery itself doesn't put out as much.
What I'd recommend is a "start from scratch" approach and find out why the amp cuts out when something else on the vehicle suddenly demands current. First of all, make sure that the amp wiring is adequate and all the connectors are tight. The recommended power and ground wire size for the amp is 8AWG. Make sure that the ground is within 3 feet of the amp and that it connects DIRECTLY to bare metal. Make sure that none of the wiring has any breaks in the insulation and that none are making contact with the vehicle body or other wires. Finally, check that you are not asking the amp to produce more power than it was designed to deliver. The minimum load impedance should be no lower than 2 ohms.
If everything on the amp is OK, then your vehicle simply cannot deliver enough current. There's several cures for that. The first would be to do the "Big Three" upgrade. Just Google "big three upgrade" and the very first result will be the www.the12v.com
install bay forum. There is a step-by-step procedure and a complete materials listing. And most of the time, upgrading the "big three" will cure low current audio problems. Changing out the battery to one with a higher amphour rating and/or installing an alternator with more output capability are also possible cures.
Hope this helps.