Those icons are called 'favicons.' They are stored in the Temporary Internet Files and when you either clear those or when the file is full and begins eliminating old files by itself, they vanish and are replaced in the Favorites by the generic icon.
While it's possible to save them from the temp files, it's a bit of a pain for something so relatively minor. There's a free program click here
that should restore them for you. (they may well vanish again next time you clear out the temp files/cache at which point run the prog again. Hope this helps :)