Solved! Go to Solution.
The clip tool does this to me often as well. I think this happens because the raster cells would not perfectly align with your polygon boundaries (it is likely the line goes through the middle or partly through cells of the raster). Therefore, when the rasters overlap, I believe the clip tool will discard those cells that go past the boundary.
An ugly solution would be have the polygons slightly overlapping (by a tolerance of at least the cell size of the raster). So if your cell size is 10 meters, you could just buffer all your polygons by 10 m (or 20 to be safe) so that whenever you run the clip tool, since the polygons will slightly overlap there *should* be no missing values between the rasters after the clip is done since they will slightly overlap themselves.
I'm willing to bet that someone else out there has a better solution. If so I would be interested in the workflow. This should do it though.