I am a RHP newbie but already a bit confused to find that a "public game" I started, 6 moves old about 4 days ago does not appear in My Games so I can't access it all.Does this happen often or is it just beginner's luck?
You've probably archived it by accident. When on my Games, click on My Archives and it should be hiding away in there.
Else, make sure you don't have any filters applied. If you do, you'd see this message above your list of games on My Games...'A filter is being applied to the games below. Please click here to return to the default view.'