ugh.. this is hard to answer because the question is to broad to answer so i'll attempt.. You have a working range for amps.. (which isnt concrete), and you have a working acceptable range for batteries' DOD cycles(depth of discharge). Typical working range of amps- 9-10v to 16-19v. So, let's say 10v-16v. That doesn't mean 10.4v, for example, is still fine. Under maximum potential output power, it will be pulling the most current. Adding the fact of low low low voltage, the time it will take for amplifier failure will increase greatly. So an amp can still die within it's operable voltage range just stressing over current draw. It's based on time. Time can be a second to whenever.. It's the context of the scenario. Batteries' DOD. The DOD cycles are higher with less discharge. Discharging 20% all the time and recharging will net the battery much longer life, many many years. AGMs have this typical life expectancy under lightest duties- 8-10yrs average til 60% life or 20yrs under complete failure. This is probably best best best case scenario though. Every time you cycle a battery, discharge then recharge, it potentially prevents it from resting at the same voltage it did from the beginning. After several hundred cycles or a couple thousand, it will only rest at 60% of what it used to. Voltage levels are not linear so 60% of 13.0v may be around 12.3v, for example, best potential. For daily usage, try not to allow your battery to have dynamic peaks where the battery drops below 12.0v. If it does, it's not bad, just, harder on the battery. Batteries subdued to drops at or below 11.4v for continuous usage over period of months are going to have a much shortened life due to abuse and high DOD.