Reducing stock and then adding water
Basically, a good stock is fairly concentrated.  In general, home cooks use too high a water to bones/veg ratio for a proper result.  So, when you leave your stock uncovered you are concentrating everything and, perhaps, getting a good result...at least one you like.  However, this is difficult to tell without knowing your recipe.  With respect to adding water back later, it is not an uncommon practice to reduce a well-made stock further, by half or more, simply for storage purposes.  Then when ready to use, water is added to bring it back to the original strength.