Hi jwsound,
You don't say what version OS X you're using. I'm using Mavericks 10.9.5. I can tell you a bit about your fav icons. I don't know if this applies to Yosemite or beyond.
Safari saves the fav icons for the sites you have visited in it's own little file. It is called WebpageIcons.db
It's in this folder under your name:: /Library/Safari
Safari will delete it without prompting you if you Reset or Clear your History. There might be other instances where it get deleted, not sure. It then creates a new "empty" file with the same name.
I got tired of Safari randomly deleting them, so I made a duplicate of the file (highlight the file and hit Command D from the Finder window). You can copy it to another spot or leave it there. Safari won't delete the duplicate.
If you have done a backup of some kind of your Library, you could search for it. If you've done a Time Machine backup, that's usually the best and easiest way to find the older file. Then just replace the empty file with your older file (copy over, delete and paste, etc)
Good Luck!