[akhtene]

It's my very personal impression, but while reading I didn't get an impression that Galadriel and Celeborn were very close. They had stayed together since the First Age. I just can't think of any other elven family which survived that long. (Am I mistaken?)And so couldn't some feelings be gone with time?
Perhaps they were good co-rulers (??), but even in this aspect Galadriel seems to me more powerful: she not Celeborn wears Nenya. So just perhaps she acted like a strong and independent woman would, and allowed her husband to decide for himself.
Now, why did he decide to stay? Galadriel was returning to the land where she was born; but Celeborn was of Sindar and felt more at home in Middle Earth. And besides, as Daniel has written, he must have felt responsible for his kingdom and subjects.