I suspect that the sandstone is allowing moisture to soak through from the outside. The best solution would be to dig the outside and install a good weeping tile system and waterproof the wall from the outside.

I do not know the difference between sand and brown and lime stones, It seems to be a mix in York county, PA...
Most of the stuff (dust) between the stones has failed, but as the stones are placed well and so massive that nothing will happen(short of an earthquake)...90% of the stones are either protected or coated and painted(externally), so other than some internal appearence and dust(lots of), there is no problem. I have been filling the deep voids with Min-expanding "Great Stuff". In the future, I will use more masonary coating where necessary.