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Some components of the sun screen could oxidize if the container were left open but if you close the container this is less likely. Source
I know there are empty bottles you can purchase for a dollar or so at a general store, and they aren't more than a few dollars, if that. IF you are the one with the open container, I would highly recommend buying an empty bottle to replace it. Or just find a new top. That may work.
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Check the expiration date. Also, sunscreen may not be effective if it’s been frozen, exposed to very high heat or direct sunlight, or if the bottle has been left open. Source
i heard you should also throw away your sunscreen from last year (you know, those half opened bottles). now that i've invested in a good sunscreen, no way i do that though.