There is usually a low battery cutoff in the menu system of the charger, what charger do you have? Also it depends on the battery cells right, so you want to take them down to about 3.4 volts per cell, but no lower than 3.2 volts per cell. If you were using a 4s as the power source I wouldn't set the low battery cutoff less than about 13v.
I also have found that just flying them gently till they get low does a better job of "emptying" them and allowing a better charge, after a few cycles they might be usable.
I have a TON of 4s batteries, most have some age, and most will scream at 14 volts or even lower when I punch to the moon, some even from full charge will do that, but once I let off it recovers quickly. given the specs of most of the kinds of stuff we build they can suck the juice pretty hard. I wonder what kind of sag recovery you see when you let off the throttle. If you watch many of the celebs out there, when they punch hard for a few seconds, you can often hear the gopro recording the low battery alarm on the quad.