I had this problem in very very first beta. hitting enter normally would bring it back up, just resized to ... well as big as a postage stamp.
Does the log also not open (I dont know if you tried) when pressing alt+l, alt+f, alt+s and so on?
You can try and look into the character setting where also the profanity filter is, I think there is an option to hide the chat log, but I aint 100% sure