I'm working with ArcGIS 10.1, and I have used a polygon with gaps (holes) inside it. Extract by mask gives an improper output with removing the horizontal section of the image where those holes are located ( As shown)
You could try to convert your polygon to raster. Best way is set up the same cell size as the other raster and snap raster in Environments. Then you can try Extract by mask again, but instead of polygon, you will use this raster.