I am editing a document with running headers. On some pages I need to edit them, but no matter how I click on these headers (or Crl-Click) I just cannot select them. I have done this in the past and then it worked. It still does work on some pages. I do not have the impression that they are blocked by other text frames. What's more, when I open the Master Page and try to edit them there I have the same problem. Yet they are functional, they appear on any page I want, only editing is not possible.
To override, you need to Ctrl (Cmd) + SHIFT click a master object, so try adding your shift key. It's possible that the master is based on another, and that's wwhere the headers really live, too, so you'd need to override on the current master to edit anything inherited.
The other possibility that comes to mind, but ti doesn't really fit your description, is that you are dealing with a variable.
Are they locked?
Good thought. I HATE the default behavior of not being able to select locked objects, so I have my prefs set to allow it, and consequently always forget it exists.