Rusting pipes aren't particularly impacted by minerals in the water. You have a leak in the system that is likely constantly adding fresh water. Fresh water brings new oxygen. New oxygen causes the iron to rust. If it was truly closed, any impurities in the water would get 'used up' and reach equilibrium with the rest of the system. No oxygen, no rusting. The pipes could last for decades if there are no leaks and no new oxygen getting into the flowing water inside the pipes. Now, water on the outside will always rust things, since the air contains more than enough to generate rust, but inside, it should be good.
Fix the leaks, your problem should go away. the path to reaching equilibrium may take longer if your water's pH is low. If that's the case, a filter to neutralize it might help, but it wouldn't be to remove minerals, it would add some to neutralize things. There are some 'conditioners' designed for this that are probably more effective that could be added when you fill the system.