From your question it seems this issue is on folders, and you do not mention any inability to access these files. If this is the case the below should apply to you:
Unlike the Read-only attribute for a file, the Read-only attribute for a folder is typically ignored by Windows, Windows components and accessories, and other programs. For example, you can delete, rename, and change a folder with the Read-only attribute by using Windows Explorer. The Read-only and System attributes is only used by Windows Explorer to determine whether the folder is a special folder, such as a system folder that has its view customized by Windows (for example, My Documents, Favorites, Fonts, Downloaded Program Files), or a folder that you customized by using the Customize tab of the folder's Properties dialog box. As a result, Windows Explorer does not allow you to view or change the Read-only or System attributes of folders. When a folder has the Read-Only attribute set it causes Explorer to request the Desktop.ini of that folder to see if any special folder settings need to be set. It has been seen where if a network share that has a large amount of folders set to Read-only, it can cause Explorer to take longer then what is expected to render the contents of that share while it waits on the retrieval of the Desktop.ini files. The slower the network connectivity to the share the longer this process can take to the point where Explorer may timeout waiting for the data and render nothing or appear to hang.
I have run into the issue you are describing in the past where you uncheck the box and after closing and opening properties again it is still checked. The above is what I found when looking into this issue.