Windows don't respond to key combinations. Menu items do. In response to being pressed (whether using the mouse, using a key combination, or using Accessibility), the menu item sends its action message down the responder chain.
You get a beep when nothing in the responder chain responds to the action message.
Assuming that this is an NSDocument-based application and you've started Apple's doc-based-app template, the menu item's action is saveDocument:
, and the NSDocument object is the object that responds to that message. When your document windows are active, their documents are in the responder chain, so the menu item that sends that action message is enabled. When your third window is active, the document is not in the responder chain; nothing else responds to that message, so the menu item is disabled.
This problem isn't specific to Save—it affects all action messages that should go through to the document object. One important other example is Print: The user will probably mean to print the document, not the third window.
You've probably made this third window a kind of window that exists as a peer to the other windows. Besides this responder-chain problem you're having, the user will also probably not realize that they have left the document; they expect to still be able to do document things. Consider making it a utility panel instead.
If you really do have a good reason to make this window whatever kind of window it is, you'll need to keep the last-active document object in the responder chain when this third window becomes main, while at the same time handling the case where the window becomes main because a document window (possibly the last one) has closed.