This worked for me in one case (even though it appeared the website had finished loading) with Safari 9.1.3 and OS X 10.9.5.
From mavericks - How can I force Safari to Save As webpage? - Ask Different:
"This can happen when the page hasn't actually finished loading. Try pressing command-[period] to stop it loading, then try saving the page."
I couldn't find any official Apple documentation regarding the function of Command-Period in Safari and none stating that Command-Period forces a webpage to stop loading. (But here Command-Period is said to Cancel current Find.) So whether a cause of Safari's File>Save As... being grayed out might be that the site hasn't finished loading is still open to question. But because this has worked for me, it suggests a line of inquiry.