American Airlines does not have any personnel in Beijing, so if you need assistance with rebooking or trying to make a flight the only way to do so is to call the United States. American outsources their check-in counter personnel to Air China, and Air China shuts down the counter early to force fliers that can make a flight to miss their flight and have to rebooked on Air China.
American only has one flight a day out of Beijing, and it's partner airlines in One World cannot get you to another destination in time to make another American flight to the US on the same day.
You will be forced to wait another day to leave China, and you will be forced to pay for all of the rebooking fees and differences in the flight costs even though Air China running the counter for American shuts the counter down early so that they can try to force you to fly Air China.
Do not fly American into or out of Beijing the cheaper flight is not worth the hassle because the likelihood of you getting screwed over and be forced to pay more than you would have to fly on United, Cathay, Air China, Korean Air, Asiana, Continential, or any other airline that has daily flights to the US out of Beijing.