A typical bottle of soy sauce won't go bad at room temperature soon after opening thanks to its fermented nature and high salt content that prevents bacteria from sprouting.
However, the flavor will start to degrade over time due to oxygen exposure. A bottle opened for two or three years will be unusable simply because it won't taste good.
While refrigeration isn't necessary, storing soy sauce in the fridge can help it stay fresh. Typically, an unrefrigerated bottle will stay fresh for around three to six months.