actually, if you left the amp connected, there IS power going through it. . .quite a lot of power in fact. really its not that much different than if you were running your subs off it. The volume you hear from your sub is the result of the small signal gain created between the signal from your headunit and the output of the woofer (very simply put, EEs on the board need not apply). However, to power a small signal amplifier, you need a substantial DC power source, so while you won't be drawing any current for small signal amplifcation, your amp is still a big resistor draining DC power from your battery. I'd check all the grounds for your new amp first and foremost, then I'd see about the wiring path you chose for the heavy guage power wire. You might have a contact, or perhaps even some interference where its really not good to have it. . .

Note that this is all null and void if you can control the remote turn on lead from your headunit while the unit is actually on. Turning the sub volume down to zero is not the same thing. . .