My 10 year old son has just experienced this unfortunately. Have been through this thread and others as well on other forums but the problem remains unresolved.
What seems to have changed is this - till recently he could log in using his nick & password. Gamecenter doesn't seem to allow that any longer, it forces you to use an apple id. When he used the apple id, the id wasn't linked to his nickname. It asked him to enter a nickname and when we tried using the old nickname, it gave an error that the nick is already in use. We entered a new nickname but all of his old data is lost.
Thing is, I can see that his old nickname & data still exists in the Gamecenter system as he's linked to my own gamecenter id as a 'friend'. so when I log in, i can see my son listed under my friends and I can see all his old data intact. His old nicname seems to have got 'orphaned' - not linked to his apple id any longer.
Seems like a longshot but if anyone has any additional suggestions, I would really appreciate it!