The Anit-Rust mechanism is pure BS,, The steel body panels are galvanized to resist rust but, there is not a cathode that I'm aware of to keep the rust bugs at bay.
Have someone you trust at a good quality parts store do a "Load Test" on your battery (Detached from the vehicle).
Your problem sounds more like a shorted cell within the battery. Depending on the brand, most batteries have a sticker over the vent holes so your don't see them. (Usually between the posts) Does said sticker have a discoloration?? If it does, that is a tell tale sign of the battery "Venting", a common occurance when a cell is shorted (Caused by deposits stretching from one plate to the other). This venting is a release of hydrogen and sulfuric acid making the discoloration.
The load test shows the defect much better than a simple voltage test. The load test will show the voltage of the battery under load (Which should drop dramatically over a short period of time) and be very different than a simple resting voltage test, which will most likely show 12 volts or just under making the service person tell you the battery is fine when it's not.
Good luck