varying sound levels from amp?

This isn't exactly a car audio project, it is a home stereo project built with car audio parts.

I'm building a stereo for my garage with some stuff I had laying around. I have a 12V sealed lead acid battery (35AH) that is wired directly to a Jensen 4 channel amp (760.4 model, 65 watts RMS per channel unbridged) with 8 gauge wire for power and negative. Hooked up I have 2 old 90 watt RMS rated Pioneer 6x9s. Instead of a car head unit, I hooked up my Samsung Galaxy 2 phone directly to the amp via a 3.5mm-to-RCA cable. Everything works fine, but on some heavier songs, the sound levels will drop during periods of heavy bass (think heavy bass guitar and bass drums pounding away during a refrain). This happens regardless if I run the amp bridged to 2 channel mode, or only run 2 of the 4 channels in 4 channel mode. Measuring voltage off the power and ground terminals of the amp, I don't detect any voltage drops when the sound levels start to become erratic.

My first thought was that the phone wasn't putting out a high enough voltage for the amp to cleanly amplify the signal during those periods . I then tried to hook up an old MP3 player. There was no varying in the sound levels, but the overall bass response wasn't as good as when I had the phone hooked up.

Here are my few theories, I was wondering if anyone had any input?

1- The power wiring is inadequate. I would find this hard to believe because the total power the amp is drawing wouldn't be over the capabilities of a 3' run of 10 gauge wire (I wouldn't think)

2- The battery just doesn't have enough juice. I find this hard to believe because I don't see any voltage drops during the heavier songs. On a full charge, I see roughly 12.7V. Is that not enough to cleanly power this amp?

3- The phone is the culprit. This is what I find to be most likely. Even though the MP3 player gave an overall lower quality of sound (what I would guess means the MP3 player puts out an even smaller voltage on the sound signal), I feel that somehow the phone self-attenuates the sound levels or has its own internal problems that cause it to drop in voltage on the output signal during extreme music. I will probably end up getting a head unit with proper RCA preamp outputs to test this, but what do you guys think?

A 35AH should last about one hour at its full 260W output (~25A).
But car systems usually see ~14V, not the 12.7V or less of a battery.

As long as you are sure it is not dropping across the battery terminals - eg. from 12.7V to 11.7V under load.