For the current/amperage to increase as voltage drops, the resistance would have to change. It's not my law. But it's Ohm's. Have you measured a resistance change in low voltage situations?
Since current is voltage divided by resistance... resistance would have to go down to increase the current. And under low voltage and/or high current apps, the resistance is likely to be higher as things heat up. No?
Unless you mean the internal resistance of the battery? Which I'm not sure is likely to drop as voltage gets lower either.
It just occurred to me that you might be thinking that becuase your electrical's voltage drops as the amperage supplied increases that you think the current increase is a function of the voltage drop. When, in fact, it's just consequential.
I'm working all of this out in my head while typing this, man. If you have something I'm missing, I'm all ears.