I think your problem is with AMEX and not Concur.
My company uses Concur with AMEX too. AMEX is responsible for the ticketing. When you reserve and pay on Concur your request goes to a queue in AMEX. They just did not get to it fast enough. Since my company requires me to go through AMEX, if I found myself needing a ticket for a flight in a few hours, I would call AMEX. I've found that they are generally pretty good.