It sounds to me like the little clip inside the socket is holding onto the lighter element too well. You might try cleaning the raised edge around the end of the element with a scotch-brite pad. I don't know what you could use to clean the clip, maybe an emery board? The clip itself might need to be widened slightly(very slightly or it won't hold at all)
(disclaimer)Be sure to remove the fuse before working on the socket.
