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Merrill is a co-founder of Food52.
All oil will eventually go rancid, but keeping it in the fridge will ensure that it stays good for quite a long time (several months) -- much better than keeping it in a cabinet at room temp.
I apologize if you already knew this, but hopefully you are not using citrus oil as an edible. Most citrus oils are irritants and their use is limited to alternate applications (solvents, cosmetics, environmentally friendly pesticides, aromatherapy), but they are not suitable for consumption. Some higher grade ones can be added in very small amounts as a flavoring agent, but be cautious what you use and how much.
I use Boyajian orange oil in small amounts as a powerful flavoring and keep it in the fridge. Smell before using - it does eventually get sad and rancid.
Perhaps the question referred to citrus infused olive oil? Both lemon and orange infused olive oil are available here in Australia and are a wonderful addition to many dishes, but as Merrill said, they will go rancid. Olive oil tends to set a little if kept in the fridge so, if possible, buy them in small amounts and use quickly. Also, don't be tempted to purchase cheap infused oils as they will be quite unpleasant and are likely to be flavoured with chemicals rather than the real flavouring.
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