As soon as you store juice away, you are allowing the oxidation process to kick in. However, you can manipulate this a little bit depending on the container that you store away the drink in. For instance, you should avoid most plastic containers as this will speed up the oxidation process. Instead, go with glass containers such as mason jars as these will seal tightly. This is the key, for the jar to be as sealed as possible.
In addition to this, it is also beneficial to fill up the glass container as high as possible. The less air that is allowed inside the jar the better it will be for your juice. What is nice about some juicers is they will come with a dedicated jar for juice storage.