Are you setting the processing extents via "Geoprocessing>Environments"?
My practice has always been to extract by mask a rough cutout portion of the our countywide DEM before starting a ArcHydro project. I originally assumed I'd need to do this to limit the processing extents. All he ESRI examples do this. A second reason to extract the local DEM is to preserve the data set. The countywide data can be updated periodically. I'd like to preserve the dataset so that if the DEM changes, I can do a comparison to see if there will be different results in the future. So I've never run into your problem.
I've had the batch processing run only for the batch point extents. (http://forums.arcgis.com/threads/41988-Resetting-Raster-calculation-limits). This was before I knew about "Geoprocessing>Environments". So in my experience, I've had the opposite problem you are having.