Just to prove there is an exception to every rule.....
I am currently on the west coast of the USA. I used United miles to get here and they booked me on Air Canada (probably no bad thing). When I booked I could only get Vancouver/Toronto/London, not the non stop. Today is Monday, I'm flying back to the UK Wednesday. A couple of hours ago I checked United (again!) to see if the non stop was available and, hey presto, it is so I've rebooked for a USD100 change fee.
So, just occasionally something will pop up at the last moment but really, don't count on it. I consider myself exceptionally lucky to have made that change.