permissions - How to only allow particular programs to modify certain files?

Windows 7, 32-bit: There is 1 user account in this PC, and that is my account.

What I do is, I right click to a folder and uncheck the read only option, apply, close. After when I reopen the folder's properties I see that it is restored and file is still read only.

What should I do?

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. Source

I've spent a lot of time trying to make my folders not read only too. Even talked to my computer support staff and they were unable to resolve it. Guess what! There wasn't anything to fix.

Did Google search and found out that while files restrict changes when it's read only, folders that are read only are read only so different programs know how to treat them (it's a bit technical for me to explain more, since that's all I understand). Kyle's answer has the more technical details about it all.

But the real eye opener was this website which had pictures. Seems that even though the read only box has a little square in it - it isn't read only. Just when the box has a check mark in it, is it read only. So all this time and energy and they weren't even read only and even if they were, it's only important to the programs to know.

Hope this is the case with you and they aren't read only, so you won't have to worry. Cheers! Here's the pictures telling which are and aren't read only.

http://www.sevenforums.com/tutorials/63741-read-only-file-folder-attribute.html

Try using the attrib tool from the command prompt. You can type attrib /? to see usage guidelines.

Try this:

attrib -r -s c:\YourFolder /S /D

-r means remove readonly attribute -s means remove system attribute /S means process files and all subfolders /D means process folders also

Are you checking files or folder? Windows ignores read-only attributes for folders. If you un-check the read-only checkbox for a folder, it just appears greyed out the next time you open the folder properties. Check the "Cause" section of this KB article: http://support.microsoft.com/kb/326549

I had a similar issue yesterday, you can try this on the folders in question:

Right click your folder
Select properties
Hit the security tab
Click the Advanced button
Click the Owner tab
Click Edit
Highlight your username
Check "Replace owner on subcontainers and objects" 
Select OK, OK

Then you can go in and check the NTFS permissions under Properties -> Security and and ensure you have full control. This should solve your files being read only.

Could you be looking at a SSD that's reached the end of it's rated life and gone into read-only mode?