I have never kept my soap covered and I have observed two negative effects:
First- The fragrance often diminishes over time.
Second- The soap shrinks and allows water to make it's way down the inside and bottom of the shaving mug.
On the other hand I have noticed that most of the higher priced soaps come in a small tub with a lid. This would probably counteract the above two negatives.
But, does not the lid method encourage mold and bacteria?