Avoiding Extract by mask error 999999?

I am iterating through ~300 raster tiles, using a polygon feature class to extract by mask. The model successfully processes the first ~100 tiles and then I get the following error on the same tile each time:

ERROR 999999: Error executing function.
The table was not found. [VAT_T2001]

ERROR 010092: Invalid output extent.
Failed to execute (ExtractByMask).

I changed the extent parameter of the extract by mask tool from default to “intersection of inputs” and got the same error for the same tile. The tool seems to work fine when I change the extent parameter to “union of inputs” but it takes an extremely long time to process each tile.

I thought that the error might be occurring because there is no overlap between the error tile and the mask feature class, but I confirmed that the tool successfully processes other tiles where there is no overlap.

The tiles and the feature class have the same spatial reference. The error also occurs for a handful of other tiles in the data set.

Does anyone know how to resolve these errors while maintaining efficient processing?

The model is just an iterator sitting in front of the extract by mask tool. So this is a question about why extract by mask works for some raster datasets and not others when the datasets have the same attributes and the tool has the same parameters.