I am trying to calculate the mean raster value within zones (vector) using the tool "zonal statistics as table". This works for the larger-area zones, but not for smaller-areas. Making the cell-size of the IDW smaller does work.

How can I determine what cell size to use?

But, I am looping through many files so would prefer to not to do this since it takes much longer.

Are there alternative tools?

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    Can you edit your question and specify if your zones are vector or raster data please. – user2856 Feb 8 at 2:59
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    You can compute largest inscribed circle using this gis.stackexchange.com/questions/147790/… but ArcGis version is very slow. I wish you can use arcview 3, because same task runs close to 50 times faster. – FelixIP Feb 8 at 6:21

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