I need to loop through the rows in the raster attribute table and add a date for each row.
Because it has an attribute table, this is a categorical raster. Why not, then, create a lookup table to match dates to categories and join the lookup table to the attribute table? You probably already have a computer-readable version of this lookup table anyway, so this procedure might save considerable time and effort as well as reduce the error rate compared to a manual alternative.
To loop using CalculateField as deskcheck1 mentions
ModelBuilder link for Iterate Row Selection http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#/Iterate_Row_Selection/004000000010000000/
*assumption using ArcGIS