The problem I had with my DS was I couldn't connect to my wireless Linksys using either wpa or wep codes (i forget whichj). Apparantly the unit doesn't support them. Perhaps that's because I have the original Clamshell DS version from '05/'06 or whatever it was when I bought it.
sounds more like you are connecting but then gettin booted? In which case, I have no clue why it would work...and then not work.
The folks @ Ninty America are really helpful and its pretty easy to get through to them. 800-255-3700