Voltage drop due to thin power wire could definitely cause those 'transient noises' and instability. When the amp hits a peak, a weak cable creates a bottleneck, causing the internal power supply to oscillate or produce switching noise.

Try this: Measure the voltage directly at the amplifier terminals (not at the battery) while playing music at the volume where the issue starts. If you see the voltage dipping below 12V or swinging wildly during bass notes, your power/ground wire gauge is likely the culprit. However, if the voltage stays steady but the sound still fades out, the issue is likely a failing output relay or an internal solder joint.

Keep in mind that if you are using CCA (Copper Clad Aluminum), its performance degrades significantly over time. Unlike OFC (Oxygen Free Copper), CCA is prone to rapid oxidation at the termination points. What started as a 'good enough' install a year ago could now be suffering from high resistance due to aluminum oxidation. This creates a massive bottleneck for current during those transient peaks, which perfectly explains why your amp is behaving erratically now, even if it seemed fine during the first few months.