do most amps automatically shut off when the battery is running low, or will they just eat up the juice until the battery is too dead to crank over the engine?
i always run my stereo without the engine on, and it can run for hours without dieing, but now im getting a much more powerful amp
if the amps dont do this on their own, are there devices that can cut the power when it gets too low?
No, there are not any, some may have a device, not many at all. If i was you i would upgrade the battery, because running your system w/ out the car on will eat up the battery like mad.