This is very odd. The only thing I can think of is checking to make sure your CFW has the internet connection in it's settngs (both the CFW and Sysnand can have different settings). Also remember that your current internet connection must be the first one.
So, my suggestion is to load up your CFW (tap the DS Profile button without holding the L button) and then open the Settings app. At this point tap the top-left internet button and then the button that says connection settings. If your internet connect is not 1, then set it up to be 1.