Today I reproduced this on my live server.
I used "Rocketlauncher" complete Joomla+Theme+Sample content packages, so if these don't work I don't expect how anything will.
I get exactly the same issue on my live server with a small adittional nugget of information.
Whereas on my local server, when a preset does not save nothing happens, on the live server I get an error:
Gantry Presets Saver
SAVE FAILED
It looks like the saving of the new Preset didn't succeed. Make sure your template folder and "custom/presets.ini" at your template folder root have write permissions.
Once you think you have fixed the permission, hit the button "Retry" below.
If it still fails, please ask for support on RocketTheme forums
I have also noticed a slight variation of the problem on Radiance. On this theme, choosing a new background will also allow you to save.
I can provide an admin account so you can verify this for yourself.