The following is entirely speculation as I have no knowledge of the processes involved but I would presume this is a synchronisation issue between Amadeus (BA) and Sabre (AA).

By 'Confirmation Code' do AA mean the PNR or some other kind of system code? Clearly there's an Amadeus PNR in BA's Manage My Booking functionality but one assumes an instruction needs to be passed from Amadeus to Sabre to trigger the creation of the booking details and generate a separate PNR in AA's system.

If Sabre somehow has the flight details for the AA sectiors but no 'local' PNR to drive the seat selection process on AA's website this may require BA to reconfirm/reissue the ticket in Amadeus to force the PNR to generate on the AA side (the equivalent of "hit it again to get it working")

If this is a new booking made this weekend I might also give it 24-48 hours to fix itself due to 'weekend flakiness' (or any back-end maintenance) impacting updates between the two systems, assuming date of travel isn't for this week.