Ganesh,
Did you reset your processing extents via Geoprocessing>Environments>Processing Extents as I mention in my Feb 26, 2015 8:52 AM post to Ryan (above). When I see a raster "cut off" like that, my first thought is the processing extents got messed up. My most memorable situation was when the limits of the resulting dem were a rectangle that matched the extents of the BatchPoints I was using. I'm not sure what part of the Arc Hydro process might change the processing extents.
However, it could be that the values are NOT cut off. The white area could be positive numbers in your highest elevation classification. If you classify with a different color ramp you will likely see that the white area is not "blank" as happens when the extents are wrong. Maybe one of the intermittent steps resulted in a cut of one of the intermittent rasters due to the extents changing and subsequent steps reflect that "missing" part of that cut off DEM.
In your case something looks really strange because your elevation values in the AgreeDEM are very negative in general and you have "spots" all over that are dark making me think they are negative. I've never seen this before.
A step I take sometimes is to use the Spatial Analyst tools like raster calculator on the SA toolbar (you have to add it to the toolbar) to subtract one raster from the other (Agree DEM - rawdem). In a normal situation this will show you where the process has raised or filled in the DEM. This is really handy to see places you may need to add a stream such as at a culvert embankment that "blocks" a stream. Occasionally this will reveal something you couldn't see otherwise.
Sorry I can't be of more specific help. If I were you I'd make sure to save the agreestream, innerwalls, outerwalls, batchpoints and rawdem layers, etc., and delete everything else and start in a fresh mxd. When I do this I delete the folders, geodatabases and all. This would make sure the extents, tempfile locations, target locations, etc. are all set. They should be setup again automatically by the Arc Hydro process. Coordinate systems need to also match. I have not dealt with a vertical datum conflict issue and that is one very remote possibility, especially seeing how your elevations "inverted" for some reason.
Best,
Mark