I am an Elite, often full fare F flier. This hangup thing has happened to me before too. I am truly shocked that they do that. It is certainly not "best in class" service and as the world's largest airline there is no excuse for them to simply hang up on people and say "call back later" with an automated message.

Though I do think calling back is better than making you wait for hours, THEY should call back. I work with several companies that, when they have busy problems, have a system that allows you to enter a number where they can call you back when they are free. This would be a much better way to handle their call load problems. Otherwise outsource to India like United does.