What is being described here is a case of sweat-induced corrosion. For this to occur, sweat must be introduced into the battery compartment and bridge the positive and negative terminals of the battery. Salty sweat serves as the electrolyte which promotes ionic conduction, causing the battery to corrode. This corrosion reaction is very aggressive - severe rusting can be observed in a matter of minutes. This problem is mostly associated with BTE aids because the location of the aid causes easy sweat access.
While there are several solutions to this problem that may seem logical, they just don't work. The first, substituting the iron in the hearing aid batteries with nickel-plated titanium is cost prohibitive. The second, encapsulating the negative/positive terminals to discourage bridging, would cause a significant reduction in battery life. Attempting to waterproof the aid would cut off the oxygen supply that zinc air batteries need.
In conclusion, the best way to avoid rust is to be aware of situations when sweat could be introduced into the battery compartment. Try to avoid these situations and you should see a great decrease in the rusting of your hearing aid batteries.