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Not long. Once neem oil has been stirred into water it starts to separate again within minutes, and after a day or two the mix has lost its milky look and smells stale. Make only what you will use in one session and tip the rest away.
In the sprayer
Shake the sprayer every few minutes while you work; the oil rises to the top as it stands and the last squirts would otherwise be mostly oil. If you have to stop part-way, a mix left overnight can be shaken and used the next morning. Beyond 48 hours, start again.
The neat oil
Pure neem oil, kept cool, dark and capped, lasts a year or more. It sets solid below about 20 °C; stand the bottle in a bowl of warm water for ten minutes and it pours again. Cloudiness or a grainy texture is the oil setting, not going off. There is more on our storage and shelf-life page.
The water-soluble concentrate
Ourons water-soluble neem is pre-blended so it mixes straight into water. Keep the concentrate capped and cool and it keeps as well as the pure oil; only the diluted wash is short-lived.
Recipe and rates: how to make a neem leaf-shine spray.