It is so frustrating to lose work!
You didn't mention clicking "Done" at the bottom of the Image Options pane. I usually have to scroll down to see it, and not clicking "Done" would lead to the outcome you're seeing.
If you don't have to change other image attributes at the same time, it might be easier to use that page's Canvas Accessibility Checker to add the alt text. As it reviews errors it will take you to each image without alt text or with file names as alt text. However, it won't show you images that have bad or insufficient alt text (e.g. "Uploaded media" or "Moustache").
Accessibility Checker pane listing Issue: Image filenames should not be used as the alt attribute describing the image content. There is a box to Change alt text, a check box to mark it as a decorative image, and currently inactive buttons for Prev, Next, and Apply.
From your screenshot, I see you have TidyUp. If you also happen to have DesignPLUS from CidiLabs, then you can use its accessibility checker to edit alt text for all of the pictures on the page, without having to select each one and no need to push "Done" or "Apply". (Even images without alt text issues are shown.) That would streamline the task a little bit.
Image Alt Checker within the DesignPLUS Accessibility / Usability tab. Shows thumbnails of images. Each thumbnail has a box for Alt Text and a check box to mark the image as decorative.