What’s happening to the settings file when you make settings and exit the game?
(To know where to find your settings files, check this thread: Manually copy settings between characters and accounts )
It sounds like your pc may not be able to write to that file location.
It could also be that you have set a program to automatically synchronize your settings to another main file of another account, in which case you should either stop that or change settings using that other character. But I guess you would know if you had set up something like that in the past.
I also heard it can be impossible to save settings in that cloud computing EVE setup that CCP once tried, not sure if that’s still live and if you use that.
Can any of these things be the cause of your problem?