The best way to sanitize the rod without any possibility of damage is using Iodophor or IO-Star, both iodine based sanitizers. If you prefer to continue to use star san, you can just make a spray bottle of iodine based sanitizer for the rod and spray the rod to coat completely so you don't have to make a full 5+ gallons of sanitizer solution.
The rod can handle pHs in the 3s for short periods of time. If you are fermenting a sour or a mead, we don't recommend using a rod without some sort of protective sleeve as their pH will get into the low 3s and will damage the rod. Once you get into the 2s and upper 1s, the amount of time it takes for the rod's surface can get damaged is very small, from a few hours to even a few minutes. Concentrated star san is in the 1s so we recommend simply keeping the rod away from star san as if any concentrated star san were to make contact with the rod, you will most certainly see surface degradation.
Another great way to sanitize the rod is to unscrew it from the electronics and place it into the boil during the last 15 minutes. This will sanitize the rod nicely, and no need for iodophor.