I reported this exact behavior a few days ago. I'm still experiencing it using multiple browsers and on the app on the iPhone.

The workaround for me has been to go to aa.com, *NOT* log in, construct my itinerary, click on continue as a guest when presented with the option, then enter my name, AAdvantage number, pick seats, etc., and pay for the ticket.

Then I can log in and view the itinerary on my account. I chatted with AA (website chat) and they told me that no one else has reported this problem but that they will "look into it".