Audio Upgrades and Auxiliary Battery Issues

So I recently just purchased a base 2005 Prius, and as with any car of mine I upgraded the audio system. (Music is my life, i'm a huge audiophile). Given the install i did wasn't much for draw of power the auxiliary battery doesn't seem to be able to keep up at all. Now the head unit i have in is putting out roughly 40-50 watts rms to the speakers and the amp i have for my subs is drawing around 400, and after a period of time of playback you can hear the volume levels decrease and sometimes you'll get a lot of static and distortion in the speakers. I'm assuming this is because the small auxiliary battery these cars come with either isn't getting recharged fast enough or is just draining way to quickly in general. The battery just recently got replaced by the previous owner and is probably no more than a month old. I've seen some other threads on system upgrades on here but i didn't see anyone mention this issue. I'm hoping someone can shed light onto some possible solutions, or if there is an upgrade for a higher output battery that i could purchase.

Thank you in advance for any responses