I am so glad I found this post. I have been having a problem with this too. I looked at the code after I pasted it onto my page and discovered that the http: was missing! Facebook created the iframe code as this:

<iframe src="//www.facebook.com/plugins/like.php?href=http%3A%2F.......................

I changed it to this"

<iframe src="http://www.facebook.com/plugins/like.php?href=http%3A%2F.............................

Problem fixed! Thank you Margaret for finding and sharing this!