The PSP can't handle certain WPA2 key settings. I forget the specifics since it's been a while but I went through headaches because of this too. Sure you can disable or downgrade your security, but I like having security. In the end I gave up and just started downloading everything on my PS3 and copying it over USB (which in a way is nicer since the PS3 can actually do other things while it downloads in the background, unlike the PSP...). It's not like there are any PSP games I actually play online.
Fortunately the Vita does not have this problem. It has worked with everything I've thrown it at so far.