Still having the issue, however what worked for me was in addition to turning off the save in background, export in background and increased the recovery save time, I also turned off the enable wacom setting in the devices.
Not ideal, but seems to be working for the time being.

Beta 29.9.6 does seem to solve the issue caused by the progress bar that never disappears.

I only tested it using the file that always triggered the error in Illustrator 29.7.1 and 26.6.1 for me. I had 'Optimize Save for Performance' and 'Save in Background' preferences both ENABLED and there was no issue with Save or Save As.

https://www.dropbox.com/scl/fi/44o4u7cjue7lwyunkvbtp/Error-Test.ai?rlkey=dmgzdmey3xv0t0nvn46ne2nw4&dl=1

Ok, disregard the Ruler Display Error. Somehow, during the multiple attempts to save the file as shown in the screen recording, the file was enlarged beyond the actual 24" x 36" artboard size. Meaning, everything (artboard and artwork) was scaled up to the maximum allowable size within Illustrator, and I couldn't resize it. But the zoom in/out bug persisted.

While I was going to just post about the one issue of the latest version of Illustrator (v 29.7.1) not properly showing that a file has been successfully saved by removing the asterisk from the file name in the file tab, I discovered that while recording the error, now the zoom in/out keystroke doesn't work and in addition the ruler display has an error. See screen recording: https://nic.box.com/s/ailcm8o50nlw4xx6nbcso9491p6l0y4f

I am on macOS Sequoia 15.6

I'm having the same error in 29.7.1 on Windows 10.
Resetting preferences and rebooting doesn't solve it.

For me, if a progress bar appears and shows as complete, but never finishes, that's game over!
- Clicking Stop / Cancel makes the progress bar disappear, but .ai saving won't work again until I reboot Illustrator (can't even make and save a new file)

- Save does nothing after the progress bar error (the asterisk after .ai never disappears)
- Save As / Save a Copy / Save As Template lets you go through all the dialogues without showing an error, so you may think they've worked, but they don't actually save anything (.ai / .eps / .pdf.

Below is a link to an .ai file which reliably triggers the error for me across two computers.
It contains a single text box with overflowing text in Acumin Variable Concept at two different sizes.
It was saved from Illustrator 29.7.1 on Windows 10.
I've tested and confirmed the file produces the error on:
- Computer 1: Windows 10 - Illustrator 29.7.1
- Computer 1: Windows 10 - Illustrator 26.6.1 (downgraded from Illustrator 29.7.1)
- Computer 2: Illustrator 26.6.1 (yet to be updated to Illustrator 29.7.1)

https://www.dropbox.com/scl/fi/44o4u7cjue7lwyunkvbtp/Error-Test.ai?rlkey=dmgzdmey3xv0t0nvn46ne2nw4&dl=1

To see the everlasting progress bar dialogue:
- Open the linked File
- File > Save As > Different file name.
or even
- Select All (Shortcut > Delete > Save (Shortcut)

- The progress bar will complete, but never disappears
* Check your save target folder, the file has saved)
- Click the "Stop" Button until the progress bar disappears
- Now Illustrator is broken.
- Save As / Save a Copy / Save As Template attempts will not save a file (.ai / .eps / .pdf)
- Make a change and Save will not update the saved file
* Export As... .PDF doesn't work.
* Export As... .SVG does work, but the progress bar will stay until you hit the "Stop" button (several times).

I got this error one time when trying to cut and paste the text from the broken file to a new file:

Adobe Illustrator Alert
Can't paste the type.
ID: -128

Hopefully this is some useful info for your team to fix this devastating bug!

The workarounds in the comments didn't work for me.

The only ways I've found to save anything after the error happens is Save As / Export As SVG / Compressed SVG
- Watch your target Save / Export folder and you'll see if the .svg file(s) appear.
- In Illustrator, the progress bar will stay until you click the "Stop" button (several times).
This format doesn't keep all the info of an Illustrator file, but it might help you keep some progress at least!

Another workaround that works for me — is to Save Aa instead, rewriting the existing file.

Francisco, please try to disable Optimize Save for Performance and / or its parent option, Save in Background, in Preferences > File Handling — and see how it goes.
Please drop a comment after some time passes. The team is aware of the problem, but they need more data.

Files save status (*) asterisk in title bar/filename does not seem to work anymore. The little asterisk by the filename used to tell you if changes had been made to the open file. After a Save or Save As the asterisk would disappear. Now, it seems to always be there. If I do a Cmd-S to save and then a Cmd-W to close, the software still prompts for a save, even though no changes have been made. This is different than the behavior in previous versions.