Now its working OK, 14 hrs. later. Nothing I did to fix it.
BTW, when it does get to "Analysis saved" it stays light green. Only after new edits are made the button becomes active, turns dark green, and says "Save analysis"....
Chrome Version 146.0.7680.184 (Official Build) (64-bit)
I've been having the same issue with my daily games, but I think I found a workaround.
( copied from my bug report: )
1. It might help to delete everything in Saved Analysis (via Game History page). I cleared my browser cache too. (edit: maybe not necessary - I have saved analysis and it still works)
2. Wait until one of your daily games ends (to stop it saving the analysis, delete it before it ends - deleting works for me even when saving doesn't). (edit: deleting analysis maybe not necessary)
3. Don't review the game (or any game). This is the main point. It seems that a daily game ending fixes the bug, and reviewing a game breaks it, though I haven't tested it much. Doing post-game analysis seems to be fine, as long as you don't do a Game Review. It might be because reviewing a game saves it to your Saved Analysis, even if it didn't have any.
I'm using the latest version of Chrome on Windows 10. I also had the same problem in Edge a few months ago.
Why do my game notes, not engine analysis, sometimes get stuck like this? I can still edit more moves, it just won't save when the window gets closed. When it happens, it keeps doing the same thing even for other games...I've cleared all cache files and settings, restarted my machine, etc. The only way I know to get it back to normal, with "Analysis saved" in dark green working, is to try again at a later time. (Web, both Chrome and Firefox)