command S does not work in Indesign

Usually when a keyboard shortcut doesn't work correctly in inDesign it means that some other program or even a system plug-in or extension is using that shortcut and is thus overriding InDesign's use of it. As unlikely though as this scenario seems for Command-S—which as far as I know is universally used for saving documents—it may be worth doing the usual trouble-shooting method for a conflicting shortcut just in case.

To begin with restart the computer and when it reboots make sure that no other program or third party system extension is running in the background. Then launch InDesign and see if Command-S is now working. If it does now work then try launching other programs one at a time until you find the one that causes the shortcut to stop working. If it is possible to change the shortcut in that program then the issue is resolved. If you can't change it there then you could establish a new key command in InDesign using Edit>Keyboard Shortcuts. If none of this work and you've tried Steve's suggestion to reset preferences and caches without success then there may be a problem with your system itself.

Tell us more about your system: Please tell us what operating system (exactly) you're running. Please tell us (exactly) what InDesign version you're using. Did you make some change in your system?

Does it happen in all or just one file?

If just one file, there could be corruption: See if you can do a Save As and choose InDesign CS4 or Later [IDML]. It that works, reopen the IDML file.

If that doesn't work, or if you're having problems with all files, restore your InDesign preferences and caches:

https://www.rockymountaintraining.com/adobe-indesign-rebuilding-preferences-cache/