Could be the alternator not charging the battery properly. The battery may need to be reconditioned... Optimas are bad for that... it's not good to let a deep cycle drain or die too often... it affects the life cycle and recharge rate of the cells.
I would suggest starting the car, and then disconnecting the battery while it's running. If the car stops... then your alternator is no good.
Try another battery, try reconditioning your existing battery.
To test if there is a power drain, take a test light, disconnect the power wire of your stereo system, turn off your dome light, then disconnect the positive terminal on your battery. Put the test light inline with the power wire. So one end of the test light goes to the positive terminal (which is disconnected from the battery) and the other end of the test light touches the positive terminal on the battery itself. If there is a power draw the test light will light up. If it lights up, start disconnecting or unplugging aftermarket accessories one by one until the light goes off.
In my opinion, I would suggest going with a Kinetik Power Cell as opposed to the Optima, look at rewinding your stock alternator or replacing with a high output alternator (Ohio Generator), get rid of the 12 farad cap... especially if you get a Kinetik Power Cell.
Capacitors are 70% filter and 30% storage device... it's good to have a 1 farad cap inline with the system to use as a filter, but not worth the $ as a storage device. 1 Kinetik 1400 is more than 200 Farads of capacitance. Check
www.kinetikaudio.com
Hope this helps,
Nick