It is either connections or your electrical system. I think that since it works most of the time until you turn it up, that you are losing power. I think that it is because your alternator is being taxed and your battery cannot support it, hence a new battery (better electrical properties) would better support it.
The amps are going into undervoltage protection most likely, because the voltage is dropping during transient demand. The other possibility is that the gains are set too high and the amp is clipping and going into overcurrent protection. I would have your battery checked. The Wal-mart batteries aren't bad per-se but if it is old or has been deeply discharged then it could be on its way out and causing a drain on the alt.
i run a wal-mart batery, everstart max1nn 875cca/1000ca, it was actually rated #1 in consumer reports overall as well as drain/recharge properties PLUS only like $65
I just recently went out and bought a optima yellow top battery 34/78.In just a day I can already tell the difference.My car starts better in the morning and I can turn my music up a little more now.My lights still dim.But Im off to a good start.
if your going to consider getting an HO alt. i suggest looking at getting yours rebuilt first. i got mine upgraded from a 120a (stock) to a 180a for $160 at a local alt. shop. if you looking to fix power problems, and have upgraded wiring already and have a decent battery, then start where the power comes from and upgrade from there.