Removing the refill bottle from your Kuvée bottle after pouring will help significantly prolong the life and quality of your wine. The only time your refill bottle is "open" is when it is placed into your Kuvée bottle, as this is the only time the wine can get out. This means oxygen can get into the bottle, which ages the wine.
Too much exposure to oxygen is what turns wine bad. We're all about quality, and want to make sure you enjoy each glass of wine. To ensure your wine stays fresh, just remove the refill when you're done pouring to keep enjoying it for weeks to come.