yes, Ray, you can. Mine actually become unsnapped all the time, due to me pulling the lamp around to make it rotate on its base. I just snap them together again. Mind you, the little round snapper "studs" are pretty tough and you have to push/pull really hard- so just be careful not to bend the arms when you do this.
They were designed by Richard Sapper to be snappable :) The technology of the whole lamp is kind of experimental and ironic, and in some ways it doesn't work. But hey, that's why I like it :)
Tom in London, November 2009
