That's a smart move not to close the file -- you have more options.
There have been other reports like this, and I think updating InDesign to the newest patch is supposed to correct it. What version are you using now, and what OS?
As far as options, can you export to IDML? Do that if you can, then open the IDML and save with a new name. As a last resort you can force-quit InDesign with the file open and restart. Auto-recovery should kick in ad open the file in the same, or nearly the same, state, and then you should export to IDML.
Here are other similar threads that might offer some other clues: https://www.google.com/search?q=indesign+can%27t+save+or+undo+site:forums.adobe.com&sa=X&v ed=0ahUKEwj4gsq9jPzKAhUJJx4KHV…
For anyone else who might also experience this bug... (I think it was a bug) I was operating from 10.11.3 (El Captain) and had not upgraded the InDesign (yet) CC 2015.
When I was working on the file, an object suddenly rotated. I was unable to 'UNDO'. At that point several options were greyed out - like SAVE.
I went onto live chat with Adobe, but there was no solution. While on live chat, I tried to save as an IDML but this crashed InDesign. That file would not open. The auto recovery kicked in and I had only lost one page of work, so that was not too devastating.
Another document later in the day had the same mysterious spontaneous rotation and then non-responsive elements. So.... I have now upgraded. Fingers crossed it's all fixed.