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Store neem oil somewhere cool and dark with the cap screwed tight. A kitchen cupboard away from the oven is ideal; a windowsill or a greenhouse shelf is not.
Kept like that, an unopened bottle lasts two to three years, and an opened one twelve to eighteen months. Warmth and light shorten that, and the first sign is a change in smell, from nutty and sulphurous to sour.
A blend keeps for less time than the pure oil, because the carrier sets the shelf life. Mix small batches, label them with the date, and do not store anything you have diluted with water; a wash is mixed fresh and used within 48 hours.
The oil will set solid in a cold cupboard. That is normal; warm the bottle in hot tap water and it pours again.