Sure, you’ve heard that wine should always be stored on its side. But grocery stores and even many wine shops display their bottles upright.rong. Storing wine in the vertical position, especially if you’re trying to age it, is a big mistake that can ruin your wine. Here’s why: your wine shares a fickle friendship with oxygen. Oxygen reacts with the chemicals in your wine to change its flavor compounds. In other words, without oxygen, wine could not age.