Connecting to WPA networks with a DSi is only possible when using DSi games or DSi Enhanced games (and DSiWare, the DSi browser and the DSi shop, of course). There is no way to connect to WPA networks with DS games on a DSi, and DSi flashcards are still essentially DS games, so they can't use WPA connections. DS games have to use WEP or unsecured connections, sadly. Although now that I'm typing this, weren't online features (aka Nintendo WFC) for all DS/DSi/Wii games shut down a couple of months ago? Are you using any games or homebrew that didn't make use of Nintendo WFC for their online features?
From what I recall, DSi enhanced features and DSi games only ever worked on the CycloDSi, as you mentioned, but I also recall that it never really worked well.