If you try to save on a different location on your computer does this problem persist?
There was a known bug like this, but it should have been fixed. What is the exact version of InDesign and your OS?
I have the same problem. Sometimes i can’t save the document because "save" is grayed out.
At which version of Indesign should the bug fixed?
I use Indesign 2015.4 and ElCapitan.
I found out that if you have not made any changes to document the "Save" will be grayed out. Try making a change and see if you can save.