I had a loose connection on one once that caused the same thing. Everytime my wife would dry her hair, you could smell something burning and it wasn't the dryer. Finally found the source was the other plug in the bathroom, not even the one she was using. Both were on the same circuit but the one that was first in line had the lose wire and burned up.
The cause was probably a loose connection ... but unfortunately, GFCI receptacles have a history of faulting inside the housing. I have seen several do what I think you have described. I ahve also seen them just quit working. The newer GFCI receptacles are supposed to be manufactured so that if they fail internally the curcuit will open. I ahven't seen any reliability reports on these yet.
Was a common problem when they were wiring mobile homes with aluminum as the wire would soften and result in a loose connection which resulted in burning the home down. Most likely a loose connection but could have been a fault receptacle.