I recently updated to the latest Illustrator (26.5). Illustrator saves my file, but gives message that it hasn't saved, and the asterisk remains near file name. I can save a copy just incase it hasn't saved. Sometimes it won't save my changes. I'm not sure if the file is corrupt or if this is a new Illustrator bug.
I save to my main computer HD project folder, no place odd. I have saved as a different file name but it still wouldn't save. Then I made a new file and coppied all the art to the new file. It still wouldn't save. I saved a copy, and opend it, and it appeared to have all my art intact. So, as a way to backup, that's the way to do it.
Solved (maybe). I turned off the 'save in backround' under preferences, and it has saved the file. I no longer have the asterisk next to the file name. I think that might have fixed it. It's saving as expected now!
To be safe, I would save as and for example add a 2 to the end of the filename. The file might be locked, or some confusion over this cloud version local version. I would also turn off pdf compatible unless you absolutely need. Important to know if this is a false error about the asterisk, so please get back to us and we can help you better, after saving version 2 as a safety net.
After file is safely saved, you can restart your computer system, not sure what you are running, to clear up anything in cache which migth be conflicting. If this returns we will show you how to reset the OOBE.