Why can't I edit this Google Site?
Q: "Why is it that sometimes I can edit my Google Site and other times I can't?"
A: For reasons that aren't really clear, sometimes Google doesn't know to show you the edit buttons unless you access the Site you're trying to edit via this specific pathway:
Your Gmail screen -> "Sites" in the black bar at the top -> navigate to the site in question
If you follow a bookmark or link directly to the site, you may not see the editor, because it doesn't know you're you. (shrug)