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I saw your posting and would like to try and help.
Right off hand, with this issue, I would recommend that you temporally disable the Anti-Virus. I have seen AV programs, because of this being a batch file, label an attempt to alter has a virus intrusion.
Once you disable your AV, then try to edit and save.
Now if this does not fix the issue, then do not hesitate to get back to me for more help.
Thank you and God bless.
I understand. I do usually see even new systems come with some sort of preinstalled AV from the manufacture. Most use McAfee or Norton.
With that aside, I have found some that have been set to "read-only" status, so lets check and make sure that is not the case here.
If that is not a factor, then do this. Cut and paste the Autoexec.bat file to the desktop, then edit and save, and then cut and paste back to the root folder.
If that for some reason does not work, lets reboot to Safe Mode, and then run Sysedit from a Command Prompt. This will bring up Autoexec.bat and then edit and save.
If that did not work, then lets right click on Autoexec.bat and choose Properties. Now in that window, choose the tab, Security. Now chose Edit. Find your User Name and the box to Allow, "Full Control". Now "Apply" and "Ok" all the way back out and reboot. Now try the edit.
If none of these work then get back to me for mroe to be done with this issue.
Take care and have a blessed day.