I don't know if they would cancel it but they do change their flights. We flew with ATA last July and I booked the tickets in March. When I booked I chose flights that would give us a 1hour and 10 minute layover in Atlanta. In May or June I went on the website just for fun to see how much they were selling the tickets for and discovered that the layover was going to 2hours and 40 minutes. Needless to say I was not happy. I called the res line and they told me that they do make changes at any time and that I should have booked one of the early AM flights as they generally fill up and changes are not often made. To me that sounded like a bunch of garbage but in any case I ultimately got to where I needed to be and the price was right.