Very sorry for the delay in getting back to this! The reason the Like button isn't always showing is because something is including a really old Facebook library on your page. That old library actually conflicts with Facebook's newer libraries, which implement the Like button. You'll need to remove the following line from the page, which is the old Facebook library:
Once that's gone, the Like button should become much more reliable as the conflict will be gone.
Hope that helps, but if you need anything else, just let us know!