How exactly are you opening your Skyline documents to begin with?
Are you double-clicking on the file in Windows Explorer to launch Skyline and open the file, or are you launching Skyline first and then using the "File > Open" menu item? Or some other way?
If "Save" does not seem to work, but "Save As" does, then I would imagine that the problem could be that the Skyline document is getting saved, but it is getting saved in a location that you do not expect.
Can you maybe send us some screenshots of the behavior that you are seeing?
It might help if you could send us your Skyline document.
In Skyline you can use the menu item:
File > Share
to create a .zip file containing your Skyline document and supporting files including spectral libraries and extracted chromatograms.
Files which are less than 50MB can be attached to these support requests. You can always upload larger files here:
https://skyline.ms/files.url
-- Nick