According to geologist Robert Schoch, PhD, the serious erosion on the enclosing walls of the Sphinx were formed by centuries of heavy rainfall, which weather hasn't been present at any point during the currently accepted time-frame within which the Sphinx was carved. From a purely geological perspective, the Sphinx or at least the enclosing walls must have been carved sometime at the end of the last ice age, at least to have endured that level of rain erosion.
As we see with some South American pyramids and other megalithic structures, ancient architects, engineers, and builders would build newer structures on top of preexisting structures, such as pyramids that were built on top of and integrated older pyramids. There are a few spots in the Giza plateau that have clearly visible different strata of masonry of vastly distant age; masonry with erosion comparable to the currently visible erosion on the New Kingdom buildings directly atop masonry that is centuries if not millennia older and is extremely eroded and worn. The point here is that while we might date the exterior of the Sphinx, pyramids, or other structures, if we don't verify a continuity of age throughout the structures, we might be incorrectly assuming X site is entirely Y years old because of dating done on the most recent masonry or other construction/refurbishing at the site. Many people are convinced that the Giza plateau is vastly older than we currently accept and that the current construction is mostly rebuilding or refurbishing on top of an older site.
Here's Dr. Schoch's brief page about it on his site: http://www.robertschoch.com/sphinx.html