My understanding is that if the voltage is lower or drops the power of the servo suffers, if the servo was set to give a constant output torque then i'd get why the current would increase but since its not working to attain a goal like that and rather to use the available power to produce a response I think harry is correct, I think what you are seeing is the other way around, constant load on a servo that then produces excess heat and then the system voltage drops because it takes watts to generating that heat, maybe?!