In previous versions of Audacity, the .aup project file was small, but contained pointers to hundreds of little tiny .au files kept in a _data directory. The Audacity project structure was changed in version 3.x so that the entire project is contained in a single, perhaps very large .aup3 project file database. This project database exists whether or not you explicitly save it. After you successfully save a project there is still some undo information that needs to be deleted. This final database housekeeping is performed when you exit Audacity or close the project, and can take several minutes if you have a large project or a slow drive.
In that case, it is unlikely this is a Windows Permissions or Policy issue.
To view the %appdata%\audacity directory, click on the magnifying glass in the Windows Task Bar at the bottom of your screen and type in %appdata%\audacity. To rename it, go up one level to the Roaming directory, right-click on the audacity folder then rename it (e.g., you could add the letter ‘x’).