SDI defense

So yesterday in a MP game, I was going for an economic victory and the Chinese attacked me to prevent me from building the World Bank. I rushed the Manhattan Project and then nuked Beijing, but his SDI shot down my nuke. Can anyone explain to me how SDI works? Does it only need to be built once, or does each city need its own? Is it foolproof, in that it always shoots down nukes without ever letting them by?

Never actually seen it myself but are quite sure (90%) that it has to be built in every city to prevent that city from being nuked. Also pretty sure that it works all the time.

Yeah it was definitely the first time I had seen it too. I was surprised because I was expecting him to start swearing after his capital gets nuked, then I realized it was shot down... But I still won.