This has happened repeatedly for me in ArcMap 10 - I will be creating polygons and lines using snapping and then mysteriously I am no longer able to snap to anything, no matter what i am editing.
All types of snapping are enabled, and 'UseSnapping' is checked. The ONLY thing that may be in any way related is that it happens after re-opening the .mxd after saving and closing, but this could be total coincidence (??).
While unbelievably frustrating, the way I have dealt with this in the past is to create and build up a new dataframe (i.e., start over), but this is getting to be far too laborious.
Does anyone have ANY idea why this is happening? I have searched around and can't seem to find anyone with the same problem.