How can I make steel post bases more rust-resistant?
I would spray them with a cold process galvanizing or Zinc-rich spray paint. This will prevent the rusting and can be done in place, use a wire brush to clean the rust off shake the can 2x of the instructions and recoat the area. 

I use this method after welding galvanized parts together because I grind the galvanized coating off to allow a clean weld and not have the nasties in the vapor (welding on galvanized is dangerous--if welding inside I place a fan to blow the vapors if any away).