12 inches? Are the hinges attached to anything?
Ok, let's assume you meant 1 inch and change... is there significant rust damage to the cowl and/or toeboard? If the floor is rotten, there's nothing to hold the shape of the cowl when the doors are open.
edit: It occurred to me that your hinges could be worn unevenly, so that the pins have flat spots or the holes they ride in are elongated. Try lifting the door when fully open and almost closed to see if there's a difference.
