It depends on who you ask.
Some people have said it was in response to something Millie Kirkham did vocally, but I think that's an assumption based on his saying, "Sing it, baby!" I think that was simply in reference to the fact that he's up there cracking up and she's still singing flawlessly as if there's nothing funny going on.
Others say he just cracked himself up over the "gaze at your bald head..." line and couldn't ever get over it.
Then there is the story that in response to Elvis singing that, a guy in the audience lifted the toupee' off his head to acknowledge that the question did apply to him, and that's what put him over the edge.
Whatever it was, it sure makes for an entertaining listen.