Do I need to upgrade my car battery?

I have a stock battery and alternator in my 2005 Honda civic and when my engine is running my amp is fine and doesn't go into protection mode but the voltage on my battery goes from 14.2 to 12.9 at the absolute lowest. But when my engine isn't on my amp can only play for a certain time (at most 10 seconds) before going into protection mode. It seems like it can't pull enough power from the battery. Oh and BTW my amp is 600 watts rms and I have one sub doing 600 watts rms at 2 ohms

If you can only play the system with the engine off for a few seconds I have to question the condition of the battery.

When the engine's off and the amp shuts down -- does the engine restart ok?

You need to upgrade your brain, Your car is not a music machine. This vehicle's electrical system is compromised.

Just check to make sure all wiring is correct and you have the proper fuse and wires for your system. If nothing wrong with that check the fuses on your amp. But I would strongly advise getting a second Kinetik battery or XS power battery for your system if you like to listen to the radio with the car off. Ps playing music from the amp and subs is a huge power strain on the battery with the car off