Members of a network embedding video.

As a supper admin I can embed video into a post. However, when ever I am logged in as a member and trying to create a post on that members site I can not embed either YouTube or Vimeo clips. Once I hit Publish or Update the embedded code disappears. This problem does not occur when logged in as a supper user. The supper user can even embed video on other member sites with out a problem. What's up with that? Any help is appreciated. Thanks!