It's odd that your favicon vanished on you, that part I can't explain. But what you are experiencing with uploading a new favicon happens to me all the time too, just wait a bit for the image cache to catch up. Or if you are like me and don't want to wait, or if you are dealing with a stubborn favicon, you can speed up the process by opening the favicon from your ACP (admin control panel) into a new browser window and refreshing it a few times.
I'm going to indulge an overkill step by step for anyone else that might stumble on this thread:
1. Right click the image as it appears in your admin control panel (ACP) and open it in a new browser tab
2. Open the new tab and note the URL will be something like this:
http://your-site.wikidot.com/local--favicon/favicon.gif?15006
Note that while you can see the favicon in the browser window, but it still wont appear in the tab.
3. Hit refresh a few times. There will be no change.
4. Stip the URL down to just the image removing everything beginning with the ? and then hit enter to reload the page.
http://your-site.wikidot.com/local--favicon/favicon.gif
You will no longer see your favicon, instead you will see the default wikidot favicon.
5. Refresh the page again, 3-5 times (though once should suffice)
Now the browser page will once again show your favicon. But the tab will still fail.
6. Go to the home page of your site and refresh the page a few times.
The default wikidot favicon seen in the tab will change to your new favicon.