Facebook like button is a bit cranky in my experience as well. One thing I've found is that it is very important to have a meta description for the page or blog post.
In addition to our built in Facebook like button, in the latest release (2.3.9.3) we've added the AddThis widget which combines several like buttons including Facebook and twitter, so you might try upgrading and using that to see if it works any better for you.
Hope that helps,
Joe